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Agrachev, Andreĭ Aleksandrovich

Author ID: agrachev.andrej-a Recent zbMATH articles by "Agrachev, Andreĭ Aleksandrovich"
Published as: Agrachev, A. A.; Agrachev, Andrei; Agrachev, Andrei A.; Agrachev, A.; Agrachëv, A. A.; Agrachev, Andrey A.; Agrachev, Andrej A.; Agrachev, Andrey; Agrachě, A. A.
Further Spellings: Аграчев Андрей Александрович
Homepage: http://people.sissa.it/~agrachev/
External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · GND · IdRef · theses.fr
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Co-Authors

32 single-authored
36 Gamkrelidze, Revaz Valerianovich
11 Vakhrameev, S. A.
10 Gauthier, Jean-Paul A.
8 Boscain, Ugo
7 Barilari, Davide
7 Zelenko, Igor
6 Rizzi, Luca
6 Sarychev, Andrey V.
5 Stefani, Gianna
5 Zezza, Pierluigi
4 Beschastnyi, Ivan Yu.
4 Lee, Paul W. Y.
4 Sigalotti, Mario
3 Anosov, Dmitriĭ Viktorovich
3 Biolo, Carolina
3 Caponigro, Marco
3 Charlot, Grégoire
3 Lerario, Antonio
3 Ostianu, N. M.
3 Sakharova, V. P.
2 Arutyunov, Aram Vladimirovic
2 Aseev, Sergei M.
2 Avakov, Evgeniĭ Rachievich
2 Baranzini, Stefano
2 Baryshnikov, Yuliy M.
2 Boarotto, Francesco
2 Chittaro, Francesca C.
2 Davydov, Alekseĭ Aleksandrovich
2 Kupka, Ivan
2 Liberzon, Daniel
2 Marigo, Alessia
2 Sachkov, Yuriĭ Leonidovich
2 Treshchev, Dmitriĭ Valer’evich
2 Zakalyukin, Vladimir M.
1 Bellini, Eugenio
1 Besov, Konstantin O.
1 Bogaevskij, Il’ya Aleksandrovich
1 Bonnard, Bernard
1 Bortakovskii, A. S.
1 Budak, A. B.
1 Bukhshtaber, Viktor Matveevich
1 Chakir El-A., El-H.
1 Chambrion, Thomas
1 Chtcherbakova, Natalia N.
1 Chubarikov, Vladimir Nikolaevich
1 Chyba, Monique
1 El Alaoui, El-Houcine Chakir
1 Faddeev, Lyudvig Dmitrievich
1 Gentile, Alessandro
1 Ghezzi, Roberta
1 Gonchar, Andreĭ Aleksandrovich
1 Goryunov, Victor V.
1 Grigorenko, Nikolaĭ Leont’evich
1 Gusein-Zade, Sabir M.
1 Kaimanovich, Vadim A.
1 Kashin, Boris Sergeevich
1 Kazandjian, Bettina
1 Kolesov, Andreĭ Yur’evich
1 Konovalov, Sergeĭ Petrovich
1 Kozhasov, Khazhgali
1 Kozlov, Valeriĭ Vasil’evich
1 Krasovskiĭ, Nikolaĭ Nikolaevich
1 Kryazhimskiĭ, Arkadiĭ Viktorovich
1 Kuksin, Sergeĭ B.
1 Kurzhanskiĭ, Aleksandr Borisovich
1 Letrouit, Cyril
1 Lysenok, Igor’ Geront’evich
1 Mal’tsev, Arkadiĭ Anatol’evich
1 Mishchenko, Evgeniĭ Frolovich
1 Motta, Michele
1 Neel, Robert Weston
1 Nikol’skiĭ, Mikhaĭl Sergeevich
1 Novikov, Sergeĭ Petrovich
1 Nurowski, Paweł
1 Ol’shanskiĭ, Aleksandr Yur’evich
1 Osipov, Yuriĭ Sergeevich
1 Pallaschke, Diethard
1 Paoli, Elisa
1 Remeslennikov, Vladimir Nikanorovich
1 Rossi, Francesco
1 Rossi, Tommaso
1 Rozov, Nikolaĭ Khristovich
1 Sarychev, Andrei V.
1 Scholtes, Stefan
1 Sedykh, Vyacheslav Dmitrievich
1 Sergeev, Armen Glebovich
1 Shchepin, Evgeniĭ Vital’evich
1 Shcherbakova, Nataliya
1 Shirikyan, Armen R.
1 Silveira, Pavel
1 Sinaĭ, Yakov Grigor’evich
1 Smirnov, Stanislav Konstantinovich
1 Stëpin, Anatoliĭ Mikhaĭlovich
1 Taĭmanov, Iskander Asanovich
1 Uschmajew, André
1 Vasil’ev, Viktor Anatol’evich
1 Vershik, Anatoliĭ Moiseevich
1 Vladimirov, Vasiliĭ Sergeevich
1 Volkov, Evgeniĭ Alekseevich
1 Vorobets, Yaroslav
...and 3 more Co-Authors
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Serials

20 Journal of Dynamical and Control Systems
8 Journal of Soviet Mathematics
7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
6 Russian Mathematical Surveys
6 SIAM Journal on Control and Optimization
6 Soviet Mathematics. Doklady
6 Mathematics of the USSR, Sbornik
6 Proceedings of the Steklov Institute of Mathematics
5 Journal of Mathematical Sciences (New York)
5 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya
4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
3 Matematicheskiĭ Sbornik. Novaya Seriya
3 Acta Applicandae Mathematicae
3 Calculus of Variations and Partial Differential Equations
3 Doklady Mathematics
2 Systems & Control Letters
2 The Journal of Geometric Analysis
2 Matematicheskiĭ Sbornik
1 Communications in Mathematical Physics
1 International Journal of Control
1 Mathematical Notes
1 Nonlinearity
1 Annales de l’Institut Fourier
1 Automatica
1 Functional Analysis and its Applications
1 Journal of Functional Analysis
1 Mathematische Annalen
1 Memoirs of the American Mathematical Society
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Proceedings of the London Mathematical Society. Third Series
1 Transactions of the American Mathematical Society
1 Rendiconti del Seminario Matematico
1 SIAM Journal on Matrix Analysis and Applications
1 Problems of Control and Information Theory
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 Journal of Mathematical Systems, Estimation, and Control
1 Electronic Research Announcements of the American Mathematical Society
1 Discrete and Continuous Dynamical Systems
1 Bulletin of the Georgian Academy of Sciences
1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
1 Geometry & Topology
1 Journal of Mathematical Fluid Mechanics
1 Regular and Chaotic Dynamics
1 Cambridge Studies in Advanced Mathematics
1 Encyclopaedia of Mathematical Sciences
1 ICPT Lecture Notes
1 Arnold Mathematical Journal

Publications by Year

Citations contained in zbMATH Open

133 Publications have been cited 2,618 times in 1,400 Documents Cited by Year
Control theory from the geometric viewpoint. Zbl 1062.93001
Agrachev, Andrei A.; Sachkov, Yuri L.
523
2004
A comprehensive introduction to sub-Riemannian geometry. From the Hamiltonian viewpoint. With an appendix by Igor Zelenko. Zbl 1487.53001
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
146
2020
Lie-algebraic stability criteria for switched systems. Zbl 0995.93064
Agrachev, Andrei A.; Liberzon, Daniel
89
2001
Introduction to geodesics in sub-Riemannian geometry. Zbl 1362.53001
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
73
2016
The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups. Zbl 1165.58012
Agrachev, Andrei; Boscain, Ugo; Gauthier, Jean-Paul; Rossi, Francesco
71
2009
Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039
Agrachev, A.; Barilari, D.
53
2012
Exponential representation of flows and chronological calculus. Zbl 0408.34044
Agrachev, A. A.; Gamkrelidze, R. V.
51
1978
Chronological algebras and nonstationary vector fields. Zbl 0473.58021
Agrachev, A. A.; Gamkrelidze, R. V.
50
1980
On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
50
2012
A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Zbl 1198.49041
Agrachev, Andrei; Boscain, Ugo; Sigalotti, Mario
46
2008
Navier-Stokes equations: controllability by means of low modes forcing. Zbl 1075.93014
Agrachev, Andrey A.; Sarychev, Andrey V.
46
2005
Geometric control theory. (Геометрическая теория управления.) Zbl 1078.93001
Agrachev, A. A.; Sachkov, Yu. L.
46
2004
Feedback-invariant optimal control theory and differential geometry. I: Regular extremals. Zbl 0952.49019
Agrachev, A. A.; Gamkrelidze, R. V.
44
1997
Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023
Agrachev, A. A.; Sarychev, A. V.
44
1996
Local invariants of smooth control systems. Zbl 0681.49018
Agrachev, A. A.; Gamkrelidze, R. V.; Sarychev, A. V.
43
1989
Strong optimality for a bang-bang trajectory. Zbl 1020.49021
Agrachev, Andrei A.; Stefani, Gianna; Zezza, Pierluigi
43
2002
Sub-Riemannian sphere in Martinet flat case. Zbl 0902.53033
Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I.
40
1997
Exponential mappings for contact sub-Riemannian structures. Zbl 0941.53022
Agrachev, A. A.
39
1996
Geometry of Jacobi curves. I. Zbl 1019.53038
Agrachev, A. A.; Zelenko, I.
39
2002
Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing. Zbl 1105.93008
Agrachev, Andrey A.; Sarychev, Andrey V.
32
2006
Any sub-Riemannian metric has points of smoothness. Zbl 1253.53029
Agrachev, A. A.
30
2009
Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035
Agrachev, A. A.
29
2008
Curvature: a variational approach. Zbl 1409.49001
Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca
27
2018
Sub-Riemannian curvature in contact geometry. Zbl 1376.53059
Agrachev, Andrei; Barilari, Davide; Rizzi, Luca
26
2017
Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Zbl 1327.53032
Agrachev, Andrei; Lee, Paul W. Y.
26
2014
Two-dimensional almost-Riemannian structures with tangency points. Zbl 1192.53029
Agrachev, A. A.; Boscain, U.; Charlot, G.; Ghezzi, R.; Sigalotti, M.
24
2010
Optimal transportation under nonholonomic constraints. Zbl 1175.49037
Agrachev, Andrei; Lee, Paul
24
2009
Symplectic geometry for optimal control. Zbl 0719.49023
Agrachev, A. A.; Gamkrelidze, R. V.
24
1990
The exponential representation of flows and the chronological calculus. Zbl 0429.34044
Agrachev, A. A.; Gamkrelidze, R. V.
23
1979
On the local structure of optimal trajectories in R\(^{3}\). Zbl 1057.49027
Agrachev, Andrei A.; Sigalotti, Mario
23
2003
Compactness for sub-Riemannian length–minimizers and subanalyticity. Zbl 1039.53038
Agrachev, A.
22
1998
Filtrations of a Lie algebra of vector fields and nilpoint approximation of controlled systems. Zbl 0850.93106
Agrachev, A. A.; Sarychev, A. V.
21
1987
Some open problems. Zbl 1292.49040
Agrachev, Andrei A.
21
2014
Rolling balls and octonions. Zbl 1153.70010
Agrachev, A. A.
20
2007
On abnormal extremals for Lagrange variational problems. Zbl 0826.49012
Agrachev, A. A.; Sarychev, A. V.
19
1995
On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014
Agrachev, Andrei; Gauthier, Jean-Paul
18
2001
Geometry of Jacobi curves. II. Zbl 1045.53051
Agrachev, A. A.; Zelenko, I.
18
2002
Ensemble controllability by Lie algebraic methods. Zbl 1350.93014
Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey
18
2016
Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals. Zbl 0972.49014
Agrachev, A. A.
17
1998
On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Zbl 1177.60059
Agrachev, A.; Kuksin, S.; Sarychev, A.; Shirikyan, A.
16
2007
Homology of intersections of real quadrics. Zbl 0696.55004
Agrachev, A. A.
16
1988
Topology of quadratic maps and Hessians of smooth maps. Zbl 0719.58006
Agrachev, A. A.
16
1990
Strong minimality of abnormal geodesics for \(2\)-distributions. Zbl 0951.53029
Agrachëv, A. A.; Sarychev, A. V.
16
1995
Sub-Riemannian metrics on \(\mathbb{R}^3\). Zbl 0962.53022
Agrachev, A. A.; Chakir El-A., El-H.; Gauthier, J. P.
16
1998
Solid controllability in fluid dynamics. Zbl 1141.76026
Agrachev, Andrey; Sarychev, Andrey
15
2008
Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Zbl 1068.58001
Agrachev, A.; Marigo, A.
15
2003
Systems of quadratic inequalities. Zbl 1277.14046
Agrachev, A.; Lerario, A.
15
2012
A second order optimality principle for a time-optimal problem. Zbl 0377.49014
Agrachev, A. A.; Gamkrelidze, R. V.
14
1978
Ordinary differential equations on vector bundles and chronological calculi. Zbl 0719.58033
Agrachev, A. A.; Gamkrelidze, R. V.; Vakhrameev, S. A.
13
1989
Sub-Riemannian metrics: Minimality of abnormal geodesics versus subanalyticity. Zbl 0978.53065
Agrachev, Andrei A.; Sarychev, Andrei V.
13
1999
Symplectic methods for optimization and control. Zbl 0965.93034
Agrachev, A.; Gamkrelidze, R.
13
1998
Methods of control theory in nonholonomic geometry. Zbl 0848.93012
Agrachev, Andrej A.
12
1995
An invariant second variation in optimal control. Zbl 0945.49015
Agrachev, A.; Stefani, G.; Zezza, P.
12
1998
Quadratic mappings in geometric control theory. Zbl 1267.93035
Agrachev, A. A.
12
1990
Bishop and Laplacian comparison theorems on three-dimensional contact sub-Riemannian manifolds with symmetry. Zbl 1341.53058
Agrachev, Andrei; Lee, Paul W. Y.
12
2015
On robust Lie-algebraic stability conditions for switched linear systems. Zbl 1238.93092
Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel
12
2012
An estimation of the controllability time for single-input systems on compact Lie groups. Zbl 1106.93006
Agrachev, Andrei; Chambrion, Thomas
11
2006
Control in the spaces of ensembles of points. Zbl 1447.93053
Agrachev, Andrei; Sarychev, Andrey
11
2020
Differential-geometric and group-theoretic methods in the theory of optimal control. Zbl 0542.93045
Agrachev, A. A.; Vakhrameev, S. A.; Gamkrelidze, R. V.
11
1983
On Morse theory for piecewise smooth functions. Zbl 0951.49024
Agrachev, A. A.; Pallaschke, D.; Scholtes, S.
11
1997
Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043
Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio
11
2015
Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0719.58013
Agrachev, A. A.; Gamkrelidze, R. V.
10
1989
Rigid Carnot algebras: a classification. Zbl 1125.17002
Agrachev, A.; Marigo, A.
10
2005
Controllability on the group of diffeomorphisms. Zbl 1188.93016
Agrachev, A. A.; Caponigro, M.
10
2009
Local controllability and semigroups of diffeomorphisms. Zbl 0787.93010
Agrachev, A. A.; Gamkrelidze, R. V.
10
1993
On the space of symmetric operators with multiple ground states. Zbl 1271.46056
Agrachev, A. A.
10
2011
Symplectic geometry and necessary optimality conditions. Zbl 0729.49018
Agrachev, A. A.; Gamkrelidze, R. V.
9
1991
On feedback classification of control-affine systems with one- and two-dimensional inputs. Zbl 1140.93018
Agrachev, Andrei; Zelenko, Igor
8
2007
Computation of the Euler characteristic of intersections of real quadrics. Zbl 0721.55001
Agrachev, A. A.; Gamkrelidze, R. V.
8
1988
Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0727.58009
Agrachev, A. A.; Gamkrelidze, R. V.
8
1991
On the Dido problem and plane isoperimetric problems. Zbl 0977.53068
Agrachev, Andrei A.; Gauthier, Jean-Paul A.
8
1999
On conjugate times of LQ optimal control problems. Zbl 1378.49034
Agrachev, Andrei; Rizzi, Luca; Silveira, Pavel
8
2015
Switching in time-optimal problem with control in a ball. Zbl 1386.49001
Agrachev, Andrei A.; Biolo, Carolina
8
2018
Chebyshev polynomials and best rank-one approximation ratio. Zbl 1435.15019
Agrachev, Andrei; Kozhasov, Khazhgali; Uschmajew, André
7
2020
The index of extremality and quasiextremal controls. Zbl 0587.49018
Agrachev, A. A.; Gamkrelidze, R. V.
7
1985
The control of rotation for asymmetric rigid body. Zbl 0571.70030
Agrachev, A. A.; Sarychev, A. V.
7
1983
The shuffle product and symmetric groups. Zbl 0790.05095
Agrachev, A. A.; Gamkrelidze, R. V.
7
1994
On sub-Riemann caustics and wave fronts for contact distributions in the three-space. Zbl 1040.58017
Agrachev, A. A.; Charlot, G.; Gauthier, J. P. A.; Zakalyukin, V. M.
7
2000
Switching in time-optimal problem: the 3D case with 2D control. Zbl 1379.49006
Agrachev, Andrei A.; Biolo, Carolina
7
2017
On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals. Zbl 1160.37383
Agrachev, A. A.; Chtcherbakova, N. N.; Zelenko, I.
6
2005
Local controllability for families of diffeomorphisms. Zbl 0778.93003
Agrachev, A. A.; Gamkrelidze, R. V.
6
1993
Newton diagrams and tangent cones to attainable sets. Zbl 0811.93006
Agrachev, A. A.
6
1991
Topics in sub-Riemannian geometry. Zbl 1367.53028
Agrachev, A. A.
6
2016
A second-order necessary condition for optimality in the general nonlinear case. Zbl 0386.49012
Agrachev, A. A.
6
1977
Control on the manifolds of mappings with a view to the deep learning. Zbl 1498.93033
Agrachev, Andrei; Sarychev, Andrey
6
2022
Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling. Zbl 1481.53041
Agrachev, Andrei; Boscain, Ugo; Neel, Robert; Rizzi, Luca
5
2018
Jacobi fields in optimal control: Morse and Maslov indices. Zbl 1476.58011
Agrachev, Andrei; Beschastnyi, Ivan
5
2022
On reduction of a smooth system linear in the control. Zbl 0678.49034
Agrachev, A. A.; Sarychev, A. V.
5
1987
Sub-Riemannian metrics and isoperimetric problems in the contact case. Zbl 1008.53019
Agrachev, A. A.; Gauthier, J. P. A.
5
2001
On regularity properties of extremal controls. Zbl 0951.49004
Agrachëv, A. A.
5
1995
A Hamiltonian approach to strong minima in optimal control. Zbl 0937.49012
Agrachev, Andrei; Stefani, Gianna; Zezza, Pierluigi
5
1999
Morse theory and optimal control problems. Zbl 0743.58008
Agrachev, A. A.; Vakhrameev, S. A.
5
1991
Symplectic geometry of constrained optimization. Zbl 1408.49043
Agrachev, Andrey A.; Beschastnyi, Ivan Yu.
5
2017
Continuity of optimal control costs and its application to weak KAM theory. Zbl 1203.49041
Agrachev, Andrei; Lee, Paul W. Y.
4
2010
Chronological series and the Cauchy-Kovalevskaya theorem. Zbl 0485.35004
Agrachev, A. A.; Vakhrameev, S. A.
4
1981
Level set for a smooth mapping in the neighborhood of a singular point and zeros of a quadratic mapping. Zbl 0762.46028
Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V.
4
1991
Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics. (Distorsion géodésique du volume et courbure de Ricci pour des dynamiques hamiltoniennes.) Zbl 1421.53037
Agrachev, Andrei A.; Barilari, Davide; Paoli, Elisa
4
2019
The Morse index and the Maslov index for extremals of controlled systems. Zbl 0614.58016
Agrachev, A. A.; Gamkrelidze, R. V.
4
1986
One more condition for a conditional extremum. Zbl 0693.49011
Agrachev, A. A.
4
1989
Homotopically invisible singular curves. Zbl 1377.53048
Agrachev, Andrei A.; Boarotto, Francesco; Lerario, Antonio
4
2017
Index theorems for graph-parametrized optimal control problems. Zbl 1515.49016
Agrachev, Andrei; Baranzini, Stefano; Beschastnyi, Ivan
3
2023
Control on the manifolds of mappings with a view to the deep learning. Zbl 1498.93033
Agrachev, Andrei; Sarychev, Andrey
6
2022
Jacobi fields in optimal control: Morse and Maslov indices. Zbl 1476.58011
Agrachev, Andrei; Beschastnyi, Ivan
5
2022
A comprehensive introduction to sub-Riemannian geometry. From the Hamiltonian viewpoint. With an appendix by Igor Zelenko. Zbl 1487.53001
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
146
2020
Control in the spaces of ensembles of points. Zbl 1447.93053
Agrachev, Andrei; Sarychev, Andrey
11
2020
Chebyshev polynomials and best rank-one approximation ratio. Zbl 1435.15019
Agrachev, Andrei; Kozhasov, Khazhgali; Uschmajew, André
7
2020
Jacobi fields in optimal control: one-dimensional variations. Zbl 1451.49003
Agrachev, Andrei; Beschastnyi, Ivan
3
2020
Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics. (Distorsion géodésique du volume et courbure de Ricci pour des dynamiques hamiltoniennes.) Zbl 1421.53037
Agrachev, Andrei A.; Barilari, Davide; Paoli, Elisa
4
2019
Optimality of broken extremals. Zbl 1419.49013
Agrachev, Andrei A.; Biolo, Carolina
3
2019
Spectrum of the second variation. Zbl 1422.49043
Agrachev, A. A.
2
2019
Curvature: a variational approach. Zbl 1409.49001
Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca
27
2018
Switching in time-optimal problem with control in a ball. Zbl 1386.49001
Agrachev, Andrei A.; Biolo, Carolina
8
2018
Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling. Zbl 1481.53041
Agrachev, Andrei; Boscain, Ugo; Neel, Robert; Rizzi, Luca
5
2018
Sub-Riemannian curvature in contact geometry. Zbl 1376.53059
Agrachev, Andrei; Barilari, Davide; Rizzi, Luca
26
2017
Switching in time-optimal problem: the 3D case with 2D control. Zbl 1379.49006
Agrachev, Andrei A.; Biolo, Carolina
7
2017
Symplectic geometry of constrained optimization. Zbl 1408.49043
Agrachev, Andrey A.; Beschastnyi, Ivan Yu.
5
2017
Homotopically invisible singular curves. Zbl 1377.53048
Agrachev, Andrei A.; Boarotto, Francesco; Lerario, Antonio
4
2017
Introduction to geodesics in sub-Riemannian geometry. Zbl 1362.53001
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
73
2016
Ensemble controllability by Lie algebraic methods. Zbl 1350.93014
Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey
18
2016
Topics in sub-Riemannian geometry. Zbl 1367.53028
Agrachev, A. A.
6
2016
Tangent hyperplanes to Subriemannian balls. Zbl 1351.53049
Agrachev, A. A.
1
2016
Bishop and Laplacian comparison theorems on three-dimensional contact sub-Riemannian manifolds with symmetry. Zbl 1341.53058
Agrachev, Andrei; Lee, Paul W. Y.
12
2015
Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043
Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio
11
2015
On conjugate times of LQ optimal control problems. Zbl 1378.49034
Agrachev, Andrei; Rizzi, Luca; Silveira, Pavel
8
2015
Quadratic cohomology. Zbl 1331.55003
Agrachev, A. A.
2
2015
Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Zbl 1327.53032
Agrachev, Andrei; Lee, Paul W. Y.
26
2014
Some open problems. Zbl 1292.49040
Agrachev, Andrei A.
21
2014
Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039
Agrachev, A.; Barilari, D.
53
2012
On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
50
2012
Systems of quadratic inequalities. Zbl 1277.14046
Agrachev, A.; Lerario, A.
15
2012
On robust Lie-algebraic stability conditions for switched linear systems. Zbl 1238.93092
Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel
12
2012
On the space of symmetric operators with multiple ground states. Zbl 1271.46056
Agrachev, A. A.
10
2011
The geometry of maximum principle. Zbl 1227.49026
Agrachev, A. A.; Gamkrelidze, R. V.
4
2011
Two-dimensional almost-Riemannian structures with tangency points. Zbl 1192.53029
Agrachev, A. A.; Boscain, U.; Charlot, G.; Ghezzi, R.; Sigalotti, M.
24
2010
Continuity of optimal control costs and its application to weak KAM theory. Zbl 1203.49041
Agrachev, Andrei; Lee, Paul W. Y.
4
2010
Invariant Lagrangian submanifolds of dissipative systems. Zbl 1233.37030
Agrachev, A. A.
3
2010
Dynamics control by a time-varying feedback. Zbl 1203.93046
Agrachev, A. A.; Caponigro, M.
2
2010
Well-posed infinite horizon variational problems on a compact manifold. Zbl 1204.58012
Agrachev, A. A.
1
2010
In memory of Evgenii Frolovich Mishchenko. Zbl 1302.01048
Osipov, Yu. S.; Kozlov, V. V.; Faddeev, L. D.; Anosov, D. V.; Vladimirov, V. S.; Gamkrelidze, R. V.; Gonchar, A. A.; Krasovskii, N. N.; Kryazhimskii, A. V.; Kurzhanski, A. B.; Novikov, S. P.; Aseev, S. M.; Zhizhchenko, A. B.; Treschev, D. V.; Agrachev, A. A.; Volkov, E. A.; Grigorenko, N. L.; Davydov, A. A.; Zelikin, M. I.; Kolesov, A. Yu.; Mal’tsev, A. A.; Nikol’skii, M. S.; Rozov, N. Kh.; Sergeev, A. G.; Besov, K. O.; Konovalov, S. P.
1
2010
The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups. Zbl 1165.58012
Agrachev, Andrei; Boscain, Ugo; Gauthier, Jean-Paul; Rossi, Francesco
71
2009
Any sub-Riemannian metric has points of smoothness. Zbl 1253.53029
Agrachev, A. A.
30
2009
Optimal transportation under nonholonomic constraints. Zbl 1175.49037
Agrachev, Andrei; Lee, Paul
24
2009
Controllability on the group of diffeomorphisms. Zbl 1188.93016
Agrachev, A. A.; Caponigro, M.
10
2009
Smooth optimal synthesis for infinite horizon variational problems. Zbl 1158.49039
Agrachev, Andrei A.; Chittaro, Francesca C.
2
2009
A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Zbl 1198.49041
Agrachev, Andrei; Boscain, Ugo; Sigalotti, Mario
46
2008
Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035
Agrachev, A. A.
29
2008
Solid controllability in fluid dynamics. Zbl 1141.76026
Agrachev, Andrey; Sarychev, Andrey
15
2008
Rolling balls and octonions. Zbl 1153.70010
Agrachev, A. A.
20
2007
On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Zbl 1177.60059
Agrachev, A.; Kuksin, S.; Sarychev, A.; Shirikyan, A.
16
2007
On feedback classification of control-affine systems with one- and two-dimensional inputs. Zbl 1140.93018
Agrachev, Andrei; Zelenko, Igor
8
2007
The curvature and hyperbolicity of Hamiltonian systems. Zbl 1153.37346
Agrachev, A. A.
2
2007
Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing. Zbl 1105.93008
Agrachev, Andrey A.; Sarychev, Andrey V.
32
2006
An estimation of the controllability time for single-input systems on compact Lie groups. Zbl 1106.93006
Agrachev, Andrei; Chambrion, Thomas
11
2006
The Pontryagin maximum principle 50 years later. Zbl 1122.49001
Agrachev, A. A.; Gamkrelidze, R. V.
3
2006
Vector fields on \(n\)-foliated \(2n\)-dimensional manifolds. Zbl 1244.53094
Agrachev, A. A.; Gamkrelidze, R. V.
1
2006
Navier-Stokes equations: controllability by means of low modes forcing. Zbl 1075.93014
Agrachev, Andrey A.; Sarychev, Andrey V.
46
2005
Rigid Carnot algebras: a classification. Zbl 1125.17002
Agrachev, A.; Marigo, A.
10
2005
On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals. Zbl 1160.37383
Agrachev, A. A.; Chtcherbakova, N. N.; Zelenko, I.
6
2005
Control theory from the geometric viewpoint. Zbl 1062.93001
Agrachev, Andrei A.; Sachkov, Yuri L.
523
2004
Geometric control theory. (Геометрическая теория управления.) Zbl 1078.93001
Agrachev, A. A.; Sachkov, Yu. L.
46
2004
Controllability of the Navier-Stokes equation by few low modes forcing. Zbl 1123.93020
Agrachev, A. A.; Sarychev, A. V.
3
2004
On the local structure of optimal trajectories in R\(^{3}\). Zbl 1057.49027
Agrachev, Andrei A.; Sigalotti, Mario
23
2003
Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Zbl 1068.58001
Agrachev, A.; Marigo, A.
15
2003
Strong optimality for a bang-bang trajectory. Zbl 1020.49021
Agrachev, Andrei A.; Stefani, Gianna; Zezza, Pierluigi
43
2002
Geometry of Jacobi curves. I. Zbl 1019.53038
Agrachev, A. A.; Zelenko, I.
39
2002
Geometry of Jacobi curves. II. Zbl 1045.53051
Agrachev, A. A.; Zelenko, I.
18
2002
Introduction to optimal control theory. Zbl 1034.93010
Agrachev, Andrei A.
1
2002
Lie-algebraic stability criteria for switched systems. Zbl 0995.93064
Agrachev, Andrei A.; Liberzon, Daniel
89
2001
On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014
Agrachev, Andrei; Gauthier, Jean-Paul
18
2001
Sub-Riemannian metrics and isoperimetric problems in the contact case. Zbl 1008.53019
Agrachev, A. A.; Gauthier, J. P. A.
5
2001
Principal invariants of Jacobi curves. Zbl 1239.53059
Agrachev, Andrei; Zelenko, Igor
4
2001
A “Gauss-Bonnet formula” for contact sub-Riemannian manifolds. Zbl 1044.53021
Agrachev, A. A.
3
2001
On sub-Riemann caustics and wave fronts for contact distributions in the three-space. Zbl 1040.58017
Agrachev, A. A.; Charlot, G.; Gauthier, J. P. A.; Zakalyukin, V. M.
7
2000
Sub-Riemannian metrics: Minimality of abnormal geodesics versus subanalyticity. Zbl 0978.53065
Agrachev, Andrei A.; Sarychev, Andrei V.
13
1999
On the Dido problem and plane isoperimetric problems. Zbl 0977.53068
Agrachev, Andrei A.; Gauthier, Jean-Paul A.
8
1999
A Hamiltonian approach to strong minima in optimal control. Zbl 0937.49012
Agrachev, Andrei; Stefani, Gianna; Zezza, Pierluigi
5
1999
Functional analysis - 4. Zbl 0930.00011
2
1999
Sub-Riemannian metrics and isoperimetric problems in contact case. Zbl 0986.53009
Agrachev, A. A.; Gauthier, J. P. A.
2
1999
Compactness for sub-Riemannian length–minimizers and subanalyticity. Zbl 1039.53038
Agrachev, A.
22
1998
Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals. Zbl 0972.49014
Agrachev, A. A.
17
1998
Sub-Riemannian metrics on \(\mathbb{R}^3\). Zbl 0962.53022
Agrachev, A. A.; Chakir El-A., El-H.; Gauthier, J. P.
16
1998
Symplectic methods for optimization and control. Zbl 0965.93034
Agrachev, A.; Gamkrelidze, R.
13
1998
An invariant second variation in optimal control. Zbl 0945.49015
Agrachev, A.; Stefani, G.; Zezza, P.
12
1998
Strong minima in optimal control. Zbl 0936.49014
Agrachev, A.; Stefani, G.; Zezza, P.
3
1998
Feedback-invariant optimal control theory and differential geometry. I: Regular extremals. Zbl 0952.49019
Agrachev, A. A.; Gamkrelidze, R. V.
44
1997
Sub-Riemannian sphere in Martinet flat case. Zbl 0902.53033
Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I.
40
1997
On Morse theory for piecewise smooth functions. Zbl 0951.49024
Agrachev, A. A.; Pallaschke, D.; Scholtes, S.
11
1997
Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023
Agrachev, A. A.; Sarychev, A. V.
44
1996
Exponential mappings for contact sub-Riemannian structures. Zbl 0941.53022
Agrachev, A. A.
39
1996
Generic singularities of sub-Riemannian metrics on \(\mathbb{R}^ 3\). Zbl 0843.53025
Agrachev, Andrei; El Alaoui, El-Houcine Chakir; Gauthier, Jean-Paul; Kupka, Ivan
4
1996
On abnormal extremals for Lagrange variational problems. Zbl 0826.49012
Agrachev, A. A.; Sarychev, A. V.
19
1995
Strong minimality of abnormal geodesics for \(2\)-distributions. Zbl 0951.53029
Agrachëv, A. A.; Sarychev, A. V.
16
1995
Methods of control theory in nonholonomic geometry. Zbl 0848.93012
Agrachev, Andrej A.
12
1995
On regularity properties of extremal controls. Zbl 0951.49004
Agrachëv, A. A.
5
1995
On the orbits of groups of diffeomorphisms and flows. Zbl 0902.58004
Agrachev, A. A.; Gamkrelidze, R. V.
1
1995
The shuffle product and symmetric groups. Zbl 0790.05095
Agrachev, A. A.; Gamkrelidze, R. V.
7
1994
Local controllability and semigroups of diffeomorphisms. Zbl 0787.93010
Agrachev, A. A.; Gamkrelidze, R. V.
10
1993
Local controllability for families of diffeomorphisms. Zbl 0778.93003
Agrachev, A. A.; Gamkrelidze, R. V.
6
1993
The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping. Zbl 0772.46021
Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V.
3
1992
Symplectic geometry and necessary conditions for optimality. Zbl 0776.49014
Agrachev, A. A.; Gamkrelidze, R. V.
1
1992
...and 33 more Documents
all top 5

Cited by 1,308 Authors

65 Agrachev, Andreĭ Aleksandrovich
63 Sachkov, Yuriĭ Leonidovich
40 Boscain, Ugo
29 Trélat, Emmanuel
27 Barilari, Davide
24 Le Donne, Enrico
24 Sigalotti, Mario
21 Rizzi, Luca
20 Bonnard, Bernard
16 Chitour, Yacine
16 Gauthier, Jean-Paul A.
16 Zelenko, Igor
15 Arutyunov, Aram Vladimirovic
15 Sachkova, Elena F.
14 Gamkrelidze, Revaz Valerianovich
14 Grong, Erlend
14 Prandi, Dario
13 Biggs, Rory
13 Lokutsievskiy, Lev Viacheslavovich
13 Remsing, Claudiu-Cristian
12 Caillau, Jean-Baptiste
12 Duits, Remco
12 Ebrahimi-Fard, Kurusch
12 Mashtakov, Alexey P.
12 Nersesyan, Vahagn
12 Podobryaev, Alekseĭ V.
12 Poggiolini, Laura
11 Beschastnyi, Ivan Yu.
11 Boarotto, Francesco
11 Chittaro, Francesca C.
11 Rifford, Ludovic
11 Vakhrameev, S. A.
10 Berestovskiĭ, Valeriĭ Nikolaevich
10 Grochowski, Marek
10 Manchon, Dominique
10 Markina, Irina
10 Silva Leite, Fátima
9 Baudoin, Fabrice
9 Godoy Molina, Mauricio
9 Jean, Frédéric
9 Kokkonen, Petri
9 Lerario, Antonio
9 Mason, Paolo
9 Patras, Frédéric
9 Rossi, Francesco
9 Shirikyan, Armen R.
8 Charlot, Grégoire
8 Ignatovich, Svetlana Yu.
8 Mahmudov, Elimhan Nadir
8 Vittone, Davide
7 Caponigro, Marco
7 Krasnov, Vyacheslav Alekseevich
7 Margaliot, Michael
7 Ottazzi, Alessandro
7 Pozzoli, Eugenio
7 Serres, Ulysse
7 Stefani, Gianna
7 Vallarino, Maria
6 Ardentov, Andrei A.
6 Barbero-Liñán, María
6 Basu, Saugata
6 Bauer, Wolfram
6 Bourdin, Loïc
6 Bruno, Tommaso
6 Chambrion, Thomas
6 Chyba, Monique
6 Ghezzi, Roberta
6 Greshnov, Aleksandr Valer’evich
6 Gupta, Rohit
6 Hrdina, Jaroslav
6 Jouan, Philippe
6 Khimshiashvili, Giorgi
6 Laurent, Camille
6 Li, Chengbo
6 Mamaev, Ivan Sergeevich
6 Neel, Robert Weston
6 Pinamonti, Andrea
6 Rampazzo, Franco
6 Shcherbakova, Nataliya
6 Sklyar, Grigory Mikhailovitch
6 Slyn’ko, Vitalii Ivanovich
6 Speight, Gareth
6 Tryamkin, Maksim Vladimirovich
6 Zakalyukin, Vladimir M.
5 Augier, Nicolas
5 Ayala, Victor
5 Baranzini, Stefano
5 Barrett, Dennis I.
5 Beauchard, Karine
5 Bloch, Anthony Michael
5 Cannarsa, Piermarco
5 Citti, Giovanna
5 Coron, Jean-Michel
5 Deng, Li
5 Doubrov, Boris M.
5 Durán Fernandez, Carlos Eduardo
5 Furutani, Kenro
5 Gordina, Maria
5 Hakavuori, Eero
5 Jurdjevic, Velimir
...and 1,208 more Authors
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Cited in 300 Serials

125 Journal of Dynamical and Control Systems
54 Journal of Mathematical Sciences (New York)
52 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
47 SIAM Journal on Control and Optimization
33 Systems & Control Letters
32 Automatica
29 Proceedings of the Steklov Institute of Mathematics
28 Journal of Differential Equations
23 Journal of Geometry and Physics
21 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
20 The Journal of Geometric Analysis
20 Doklady Mathematics
20 Differential Equations
19 Mathematical Notes
19 Differential Geometry and its Applications
18 Journal of Optimization Theory and Applications
18 Siberian Mathematical Journal
18 Acta Applicandae Mathematicae
18 Calculus of Variations and Partial Differential Equations
14 Automation and Remote Control
14 Regular and Chaotic Dynamics
13 MCSS. Mathematics of Control, Signals, and Systems
13 Journal de Mathématiques Pures et Appliquées. Neuvième Série
12 Journal of Mathematical Analysis and Applications
12 Journal of Soviet Mathematics
12 Potential Analysis
12 Journal of Geometric Mechanics
12 Mathematical Control and Related Fields
11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
10 Journal of Mathematical Physics
10 Annali di Matematica Pura ed Applicata. Serie Quarta
10 Journal of Functional Analysis
10 Sbornik: Mathematics
10 Discrete and Continuous Dynamical Systems
9 Transactions of the American Mathematical Society
9 Comptes Rendus. Mathématique. Académie des Sciences, Paris
8 International Journal of Control
8 Mathematische Zeitschrift
8 Journal of the European Mathematical Society (JEMS)
8 Journal of Physics A: Mathematical and Theoretical
7 Journal of the Franklin Institute
7 Nonlinearity
7 Advances in Mathematics
7 Optimal Control Applications & Methods
7 Journal of Mathematical Imaging and Vision
7 Journal of Nonlinear Science
7 Izvestiya: Mathematics
7 European Journal of Control
7 Russian Journal of Nonlinear Dynamics
6 Communications in Mathematical Physics
6 Discrete & Computational Geometry
6 NoDEA. Nonlinear Differential Equations and Applications
6 Analysis and Geometry in Metric Spaces
5 Annales de l’Institut Fourier
5 Applied Mathematics and Optimization
5 Geometriae Dedicata
5 Journal of Algebra
5 Optimization
5 Geometric and Functional Analysis. GAFA
5 Foundations of Computational Mathematics
5 Nonlinear Analysis. Hybrid Systems
5 Analysis and Mathematical Physics
4 Communications in Algebra
4 Mathematische Annalen
4 Revista Matemática Iberoamericana
4 Computational Mathematics and Mathematical Physics
4 Linear Algebra and its Applications
4 Russian Mathematics
4 Journal of Computer and Systems Sciences International
4 Bulletin des Sciences Mathématiques
4 Abstract and Applied Analysis
4 Journal of Algebra and its Applications
4 Oberwolfach Reports
4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
4 Journal of Computational Dynamics
4 Nonlinear Analysis. Theory, Methods & Applications
4 European Journal of Mathematics
4 Journal de l’École Polytechnique – Mathématiques
4 Séminaire Laurent Schwartz. EDP et Applications
3 Archive for Rational Mechanics and Analysis
3 Israel Journal of Mathematics
3 Journal d’Analyse Mathématique
3 Journal of Applied Mathematics and Mechanics
3 Letters in Mathematical Physics
3 Russian Mathematical Surveys
3 Applied Mathematics and Computation
3 Inventiones Mathematicae
3 Mathematics and Computers in Simulation
3 Pacific Journal of Mathematics
3 Proceedings of the American Mathematical Society
3 Journal of Global Optimization
3 Applied Mathematical Modelling
3 Communications in Partial Differential Equations
3 Stochastic Processes and their Applications
3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
3 SIAM Journal on Optimization
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Electronic Journal of Probability
3 Mathematical Problems in Engineering
3 Communications in Contemporary Mathematics
...and 200 more Serials
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Cited in 58 Fields

515 Differential geometry (53-XX)
470 Calculus of variations and optimal control; optimization (49-XX)
445 Systems theory; control (93-XX)
199 Global analysis, analysis on manifolds (58-XX)
183 Partial differential equations (35-XX)
127 Dynamical systems and ergodic theory (37-XX)
122 Ordinary differential equations (34-XX)
118 Mechanics of particles and systems (70-XX)
117 Topological groups, Lie groups (22-XX)
59 Quantum theory (81-XX)
53 Nonassociative rings and algebras (17-XX)
50 Numerical analysis (65-XX)
50 Fluid mechanics (76-XX)
43 Algebraic geometry (14-XX)
43 Probability theory and stochastic processes (60-XX)
38 Operations research, mathematical programming (90-XX)
34 Biology and other natural sciences (92-XX)
33 Operator theory (47-XX)
33 Manifolds and cell complexes (57-XX)
32 Abstract harmonic analysis (43-XX)
30 Real functions (26-XX)
30 Functional analysis (46-XX)
29 Measure and integration (28-XX)
22 Computer science (68-XX)
21 Associative rings and algebras (16-XX)
20 Combinatorics (05-XX)
18 Several complex variables and analytic spaces (32-XX)
16 Linear and multilinear algebra; matrix theory (15-XX)
15 Mechanics of deformable solids (74-XX)
15 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
14 Statistical mechanics, structure of matter (82-XX)
12 Geometry (51-XX)
12 Information and communication theory, circuits (94-XX)
11 General topology (54-XX)
9 Group theory and generalizations (20-XX)
9 Functions of a complex variable (30-XX)
9 Algebraic topology (55-XX)
7 Convex and discrete geometry (52-XX)
6 General and overarching topics; collections (00-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
5 Statistics (62-XX)
4 Category theory; homological algebra (18-XX)
4 Potential theory (31-XX)
4 Difference and functional equations (39-XX)
4 Approximations and expansions (41-XX)
4 Integral equations (45-XX)
4 Optics, electromagnetic theory (78-XX)
3 History and biography (01-XX)
3 Number theory (11-XX)
3 Commutative algebra (13-XX)
3 Special functions (33-XX)
3 Relativity and gravitational theory (83-XX)
2 Mathematical logic and foundations (03-XX)
2 Integral transforms, operational calculus (44-XX)
2 Classical thermodynamics, heat transfer (80-XX)
2 Geophysics (86-XX)
1 General algebraic systems (08-XX)
1 Field theory and polynomials (12-XX)

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