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Agrachev, Andreĭ Aleksandrovich

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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 · IdRef · theses.fr
Documents Indexed: 148 Publications since 1975, including 4 Books
4 Contributions as Editor
Biographic References: 1 Publication
Co-Authors: 96 Co-Authors with 115 Joint Publications
2,843 Co-Co-Authors
all top 5

Co-Authors

30 single-authored
36 Gamkrelidze, Revaz Valerianovich
11 Vakhrameev, S. A.
10 Gauthier, Jean-Paul A.
8 Boscain, Ugo
7 Barilari, Davide
6 Sarychev, Andrey V.
6 Zelenko, Igor
5 Stefani, Gianna
5 Zezza, Pierluigi
4 Lee, Paul W. Y.
4 Rizzi, Luca
4 Sigalotti, Mario
3 Anosov, Dmitriĭ Viktorovich
3 Beschastnyi, Ivan Yu.
3 Biolo, Carolina
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 Baryshnikov, Yuliy M.
2 Boarotto, Francesco
2 Caponigro, Marco
2 Chittaro, Francesca C.
2 Davydov, Alekseĭ Aleksandrovich
2 Kupka, Ivan A. K.
2 Liberzon, Daniel
2 Marigo, Alessia
2 Sachkov, Yuriĭ Leonidovich
2 Treshchev, Dmitriĭ Valer’evich
2 Zakalyukin, Vladimir M.
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 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 Kolesov, Andreĭ Yur’evich
1 Konovalov, S. P.
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 Lysenok, Igor’ Geront’evich
1 Mal’tsev, Arkadiĭ Anatol’evich
1 Mishchenko, Evgeniĭ Frolovich
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 Rozov, Nikolaĭ Khristovich
1 Sarychev, Andrei V.
1 Scholtes, Stefan
1 Sedykh, Vyacheslav Dmitrievich
1 Sergeev, Armen Glebovich
1 Shchepin, Evgenij V.
1 Shcherbakova, Nataliya
1 Shirikyan, Armen R.
1 Silveira, Pavel
1 Sinaĭ, Yakov Grigor’evich
1 Smirnov, Stanislav Konstantinovich
1 Stëpin, Anatoliĭ Mikhaĭlovich
1 Taimanov, 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, Ya. B.
1 Zarodov, V. R.
1 Zelikin, Mikhail Il’ich
1 Zhizhchenko, Alexey B.
all top 5

Serials

19 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 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

127 Publications have been cited 2,140 times in 1,146 Documents Cited by Year
Control theory from the geometric viewpoint. Zbl 1062.93001
Agrachev, Andrei A.; Sachkov, Yuri L.
388
2004
Lie-algebraic stability criteria for switched systems. Zbl 0995.93064
Agrachev, Andrei A.; Liberzon, Daniel
80
2001
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
73
2020
Introduction to geodesics in sub-Riemannian geometry. Zbl 1362.53001
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
66
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
61
2009
Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039
Agrachev, A.; Barilari, D.
48
2012
Exponential representation of flows and chronological calculus. Zbl 0408.34044
Agrachev, A. A.; Gamkrelidze, R. V.
46
1978
Geometric control theory. (Геометрическая теория управления.) Zbl 1078.93001
Agrachev, A. A.; Sachkov, Yu. L.
45
2004
Feedback-invariant optimal control theory and differential geometry. I: Regular extremals. Zbl 0952.49019
Agrachev, A. A.; Gamkrelidze, R. V.
45
1997
Chronological algebras and nonstationary vector fields. Zbl 0473.58021
Agrachev, A. A.; Gamkrelidze, R. V.
45
1980
Local invariants of smooth control systems. Zbl 0681.49018
Agrachev, A. A.; Gamkrelidze, R. V.; Sarychev, A. V.
44
1989
On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
44
2012
Navier-Stokes equations: controllability by means of low modes forcing. Zbl 1075.93014
Agrachev, Andrey A.; Sarychev, Andrey V.
40
2005
Geometry of Jacobi curves. I. Zbl 1019.53038
Agrachev, A. A.; Zelenko, I.
39
2002
Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023
Agrachev, A. A.; Sarychev, A. V.
39
1996
Strong optimality for a bang-bang trajectory. Zbl 1020.49021
Agrachev, Andrei A.; Stefani, Gianna; Zezza, Pierluigi
37
2002
A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Zbl 1198.49041
Agrachev, Andrei; Boscain, Ugo; Sigalotti, Mario
35
2008
Exponential mappings for contact sub-Riemannian structures. Zbl 0941.53022
Agrachev, A. A.
35
1996
Sub-Riemannian sphere in Martinet flat case. Zbl 0902.53033
Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I.
34
1997
Any sub-Riemannian metric has points of smoothness. Zbl 1253.53029
Agrachev, A. A.
27
2009
Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing. Zbl 1105.93008
Agrachev, Andrey A.; Sarychev, Andrey V.
26
2006
Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Zbl 1327.53032
Agrachev, Andrei; Lee, Paul W. Y.
24
2014
Sub-Riemannian curvature in contact geometry. Zbl 1376.53059
Agrachev, Andrei; Barilari, Davide; Rizzi, Luca
24
2017
Optimal transportation under nonholonomic constraints. Zbl 1175.49037
Agrachev, Andrei; Lee, Paul
22
2009
Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035
Agrachev, A. A.
22
2008
On the local structure of optimal trajectories in R\(^{3}\). Zbl 1057.49027
Agrachev, Andrei A.; Sigalotti, Mario
22
2003
The exponential representation of flows and the chronological calculus. Zbl 0429.34044
Agrachev, A. A.; Gamkrelidze, R. V.
21
1979
Rolling balls and octonions. Zbl 1153.70010
Agrachev, A. A.
19
2007
Two-dimensional almost-Riemannian structures with tangency points. Zbl 1192.53029
Agrachev, A. A.; Boscain, U.; Charlot, G.; Ghezzi, R.; Sigalotti, M.
19
2010
On abnormal extremals for Lagrange variational problems. Zbl 0826.49012
Agrachev, A. A.; Sarychev, A. V.
19
1995
Compactness for sub-Riemannian length–minimizers and subanalyticity. Zbl 1039.53038
Agrachev, A.
18
1998
Geometry of Jacobi curves. II. Zbl 1045.53051
Agrachev, A. A.; Zelenko, I.
17
2002
Symplectic geometry for optimal control. Zbl 0719.49023
Agrachev, A. A.; Gamkrelidze, R. V.
16
1990
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
Curvature: a variational approach. Zbl 1409.49001
Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca
16
2018
Filtrations of a Lie algebra of vector fields and nilpoint approximation of controlled systems. Zbl 0850.93106
Agrachev, A. A.; Sarychev, A. V.
16
1987
Strong minimality of abnormal geodesics for \(2\)-distributions. Zbl 0951.53029
Agrachëv, A. A.; Sarychev, A. V.
16
1995
Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals. Zbl 0972.49014
Agrachev, A. A.
16
1998
Some open problems. Zbl 1292.49040
Agrachev, Andrei A.
15
2014
Sub-Riemannian metrics on \(\mathbb{R}^3\). Zbl 0962.53022
Agrachev, A. A.; Chakir El-A., El-H.; Gauthier, J. P.
15
1998
Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Zbl 1068.58001
Agrachev, A.; Marigo, A.
14
2003
A second order optimality principle for a time-optimal problem. Zbl 0377.49014
Agrachev, A. A.; Gamkrelidze, R. V.
14
1978
On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014
Agrachev, Andrei; Gauthier, Jean-Paul
14
2001
Solid controllability in fluid dynamics. Zbl 1141.76026
Agrachev, Andrey; Sarychev, Andrey
13
2008
Systems of quadratic inequalities. Zbl 1277.14046
Agrachev, A.; Lerario, A.
12
2012
On robust Lie-algebraic stability conditions for switched linear systems. Zbl 1238.93092
Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel
12
2012
Symplectic methods for optimization and control. Zbl 0965.93034
Agrachev, A.; Gamkrelidze, R.
12
1998
Ensemble controllability by Lie algebraic methods. Zbl 1350.93014
Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey
11
2016
Homology of intersections of real quadrics. Zbl 0696.55004
Agrachev, A. A.
11
1988
Ordinary differential equations on vector bundles and chronological calculi. Zbl 0719.58033
Agrachev, A. A.; Gamkrelidze, R. V.; Vakhrameev, S. A.
11
1989
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
An estimation of the controllability time for single-input systems on compact Lie groups. Zbl 1106.93006
Agrachev, Andrei; Chambrion, Thomas
11
2006
Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0719.58013
Agrachev, A. A.; Gamkrelidze, R. V.
10
1989
Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043
Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio
10
2015
Bishop and Laplacian comparison theorems on three-dimensional contact sub-Riemannian manifolds with symmetry. Zbl 1341.53058
Agrachev, Andrei; Lee, Paul W. Y.
10
2015
Sub-Riemannian metrics: Minimality of abnormal geodesics versus subanalyticity. Zbl 0978.53065
Agrachev, Andrei A.; Sarychev, Andrei V.
10
1999
Rigid Carnot algebras: a classification. Zbl 1125.17002
Agrachev, A.; Marigo, A.
9
2005
Symplectic geometry and necessary optimality conditions. Zbl 0729.49018
Agrachev, A. A.; Gamkrelidze, R. V.
9
1991
Methods of control theory in nonholonomic geometry. Zbl 0848.93012
Agrachev, Andrej A.
9
1995
Topology of quadratic maps and Hessians of smooth maps. Zbl 0719.58006
Agrachev, A. A.
8
1990
Computation of the Euler characteristic of intersections of real quadrics. Zbl 0721.55001
Agrachev, A. A.; Gamkrelidze, R. V.
8
1988
Controllability on the group of diffeomorphisms. Zbl 1188.93016
Agrachev, A. A.; Caponigro, M.
8
2009
Quadratic mappings in geometric control theory. Zbl 1267.93035
Agrachev, A. A.
8
1990
On feedback classification of control-affine systems with one- and two-dimensional inputs. Zbl 1140.93018
Agrachev, Andrei; Zelenko, Igor
8
2007
On Morse theory for piecewise smooth functions. Zbl 0951.49024
Agrachev, A. A.; Pallaschke, D.; Scholtes, S.
8
1997
An invariant second variation in optimal control. Zbl 0945.49015
Agrachev, A.; Stefani, G.; Zezza, P.
8
1998
The control of rotation for asymmetric rigid body. Zbl 0571.70030
Agrachev, A. A.; Sarychev, A. V.
7
1983
Switching in time-optimal problem with control in a ball. Zbl 1386.49001
Agrachev, Andrei A.; Biolo, Carolina
7
2018
On conjugate times of LQ optimal control problems. Zbl 1378.49034
Agrachev, Andrei; Rizzi, Luca; Silveira, Pavel
7
2015
On the space of symmetric operators with multiple ground states. Zbl 1271.46056
Agrachev, A. A.
7
2011
Switching in time-optimal problem: the 3D case with 2D control. Zbl 1379.49006
Agrachev, Andrei A.; Biolo, Carolina
7
2017
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
The index of extremality and quasiextremal controls. Zbl 0587.49018
Agrachev, A. A.; Gamkrelidze, R. V.
7
1985
Local controllability and semigroups of diffeomorphisms. Zbl 0787.93010
Agrachev, A. A.; Gamkrelidze, R. V.
7
1993
On the Dido problem and plane isoperimetric problems. Zbl 0977.53068
Agrachev, Andrei A.; Gauthier, Jean-Paul A.
7
1999
Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0727.58009
Agrachev, A. A.; Gamkrelidze, R. V.
6
1991
A second-order necessary condition for optimality in the general nonlinear case. Zbl 0386.49012
Agrachev, A. A.
6
1977
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
Newton diagrams and tangent cones to attainable sets. Zbl 0811.93006
Agrachev, A. A.
6
1991
Local controllability for families of diffeomorphisms. Zbl 0778.93003
Agrachev, A. A.; Gamkrelidze, R. V.
6
1993
Control in the spaces of ensembles of points. Zbl 1447.93053
Agrachev, Andrei; Sarychev, Andrey
6
2020
Topics in sub-Riemannian geometry. Zbl 1367.53028
Agrachev, A. A.
5
2016
The shuffle product and symmetric groups. Zbl 0790.05095
Agrachev, A. A.; Gamkrelidze, R. V.
5
1994
On regularity properties of extremal controls. Zbl 0951.49004
Agrachëv, A. A.
5
1995
Sub-Riemannian metrics and isoperimetric problems in the contact case. Zbl 1008.53019
Agrachev, A. A.; Gauthier, J. P. A.
5
2001
A Hamiltonian approach to strong minima in optimal control. Zbl 0937.49012
Agrachev, Andrei; Stefani, Gianna; Zezza, Pierluigi
5
1999
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
Principal invariants of Jacobi curves. Zbl 1239.53059
Agrachev, Andrei; Zelenko, Igor
4
2001
Morse theory and optimal control problems. Zbl 0743.58008
Agrachev, A. A.; Vakhrameev, S. A.
4
1991
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
The Morse index and the Maslov index for extremals of controlled systems. Zbl 0614.58016
Agrachev, A. A.; Gamkrelidze, R. V.
4
1986
Chronological series and the Cauchy-Kovalevskaya theorem. Zbl 0485.35004
Agrachev, A. A.; Vakhrameev, S. A.
4
1981
Quasi-extremality for control systems. Zbl 0721.58014
Agrachev, A. A.; Gamkrelidze, R. V.
3
1989
Ordinary differential equations on vector bundles and chronological calculus. Zbl 0727.58042
Gamkrelidze, R. V.; Agrachev, A. A.; Vakhrameev, S. A.
3
1991
The Pontryagin maximum principle 50 years later. Zbl 1122.49001
Agrachev, A. A.; Gamkrelidze, R. V.
3
2006
Continuity of optimal control costs and its application to weak KAM theory. Zbl 1203.49041
Agrachev, Andrei; Lee, Paul W. Y.
3
2010
The geometry of maximum principle. Zbl 1227.49026
Agrachev, A. A.; Gamkrelidze, R. V.
3
2011
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
3
2019
Optimality of broken extremals. Zbl 1419.49013
Agrachev, Andrei A.; Biolo, Carolina
3
2019
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
73
2020
Control in the spaces of ensembles of points. Zbl 1447.93053
Agrachev, Andrei; Sarychev, Andrey
6
2020
Chebyshev polynomials and best rank-one approximation ratio. Zbl 1435.15019
Agrachev, Andrei; Kozhasov, Khazhgali; Uschmajew, André
2
2020
Jacobi fields in optimal control: one-dimensional variations. Zbl 1451.49003
Agrachev, Andrei; Beschastnyi, Ivan
1
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
3
2019
Optimality of broken extremals. Zbl 1419.49013
Agrachev, Andrei A.; Biolo, Carolina
3
2019
Curvature: a variational approach. Zbl 1409.49001
Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca
16
2018
Switching in time-optimal problem with control in a ball. Zbl 1386.49001
Agrachev, Andrei A.; Biolo, Carolina
7
2018
Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling. Zbl 1481.53041
Agrachev, Andrei; Boscain, Ugo; Neel, Robert; Rizzi, Luca
3
2018
Sub-Riemannian curvature in contact geometry. Zbl 1376.53059
Agrachev, Andrei; Barilari, Davide; Rizzi, Luca
24
2017
Switching in time-optimal problem: the 3D case with 2D control. Zbl 1379.49006
Agrachev, Andrei A.; Biolo, Carolina
7
2017
Homotopically invisible singular curves. Zbl 1377.53048
Agrachev, Andrei A.; Boarotto, Francesco; Lerario, Antonio
4
2017
Symplectic geometry of constrained optimization. Zbl 1408.49043
Agrachev, Andrey A.; Beschastnyi, Ivan Yu.
2
2017
Introduction to geodesics in sub-Riemannian geometry. Zbl 1362.53001
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
66
2016
Ensemble controllability by Lie algebraic methods. Zbl 1350.93014
Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey
11
2016
Topics in sub-Riemannian geometry. Zbl 1367.53028
Agrachev, A. A.
5
2016
Tangent hyperplanes to Subriemannian balls. Zbl 1351.53049
Agrachev, A. A.
1
2016
Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043
Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio
10
2015
Bishop and Laplacian comparison theorems on three-dimensional contact sub-Riemannian manifolds with symmetry. Zbl 1341.53058
Agrachev, Andrei; Lee, Paul W. Y.
10
2015
On conjugate times of LQ optimal control problems. Zbl 1378.49034
Agrachev, Andrei; Rizzi, Luca; Silveira, Pavel
7
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.
24
2014
Some open problems. Zbl 1292.49040
Agrachev, Andrei A.
15
2014
Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039
Agrachev, A.; Barilari, D.
48
2012
On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030
Agrachev, Andrei; Barilari, Davide; Boscain, Ugo
44
2012
Systems of quadratic inequalities. Zbl 1277.14046
Agrachev, A.; Lerario, A.
12
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.
7
2011
The geometry of maximum principle. Zbl 1227.49026
Agrachev, A. A.; Gamkrelidze, R. V.
3
2011
Two-dimensional almost-Riemannian structures with tangency points. Zbl 1192.53029
Agrachev, A. A.; Boscain, U.; Charlot, G.; Ghezzi, R.; Sigalotti, M.
19
2010
Continuity of optimal control costs and its application to weak KAM theory. Zbl 1203.49041
Agrachev, Andrei; Lee, Paul W. Y.
3
2010
Dynamics control by a time-varying feedback. Zbl 1203.93046
Agrachev, A. A.; Caponigro, M.
2
2010
Invariant Lagrangian submanifolds of dissipative systems. Zbl 1233.37030
Agrachev, A. A.
2
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
61
2009
Any sub-Riemannian metric has points of smoothness. Zbl 1253.53029
Agrachev, A. A.
27
2009
Optimal transportation under nonholonomic constraints. Zbl 1175.49037
Agrachev, Andrei; Lee, Paul
22
2009
Controllability on the group of diffeomorphisms. Zbl 1188.93016
Agrachev, A. A.; Caponigro, M.
8
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
35
2008
Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035
Agrachev, A. A.
22
2008
Solid controllability in fluid dynamics. Zbl 1141.76026
Agrachev, Andrey; Sarychev, Andrey
13
2008
Rolling balls and octonions. Zbl 1153.70010
Agrachev, A. A.
19
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.
1
2007
Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing. Zbl 1105.93008
Agrachev, Andrey A.; Sarychev, Andrey V.
26
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.
40
2005
Rigid Carnot algebras: a classification. Zbl 1125.17002
Agrachev, A.; Marigo, A.
9
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.
388
2004
Geometric control theory. (Геометрическая теория управления.) Zbl 1078.93001
Agrachev, A. A.; Sachkov, Yu. L.
45
2004
Controllability of the Navier-Stokes equation by few low modes forcing. Zbl 1123.93020
Agrachev, A. A.; Sarychev, A. V.
2
2004
On the local structure of optimal trajectories in R\(^{3}\). Zbl 1057.49027
Agrachev, Andrei A.; Sigalotti, Mario
22
2003
Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Zbl 1068.58001
Agrachev, A.; Marigo, A.
14
2003
Geometry of Jacobi curves. I. Zbl 1019.53038
Agrachev, A. A.; Zelenko, I.
39
2002
Strong optimality for a bang-bang trajectory. Zbl 1020.49021
Agrachev, Andrei A.; Stefani, Gianna; Zezza, Pierluigi
37
2002
Geometry of Jacobi curves. II. Zbl 1045.53051
Agrachev, A. A.; Zelenko, I.
17
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
80
2001
On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014
Agrachev, Andrei; Gauthier, Jean-Paul
14
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.
10
1999
On the Dido problem and plane isoperimetric problems. Zbl 0977.53068
Agrachev, Andrei A.; Gauthier, Jean-Paul A.
7
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.
1
1999
Compactness for sub-Riemannian length–minimizers and subanalyticity. Zbl 1039.53038
Agrachev, A.
18
1998
Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals. Zbl 0972.49014
Agrachev, A. A.
16
1998
Sub-Riemannian metrics on \(\mathbb{R}^3\). Zbl 0962.53022
Agrachev, A. A.; Chakir El-A., El-H.; Gauthier, J. P.
15
1998
Symplectic methods for optimization and control. Zbl 0965.93034
Agrachev, A.; Gamkrelidze, R.
12
1998
An invariant second variation in optimal control. Zbl 0945.49015
Agrachev, A.; Stefani, G.; Zezza, P.
8
1998
Strong minima in optimal control. Zbl 0936.49014
Agrachev, A.; Stefani, G.; Zezza, P.
2
1998
Feedback-invariant optimal control theory and differential geometry. I: Regular extremals. Zbl 0952.49019
Agrachev, A. A.; Gamkrelidze, R. V.
45
1997
Sub-Riemannian sphere in Martinet flat case. Zbl 0902.53033
Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I.
34
1997
On Morse theory for piecewise smooth functions. Zbl 0951.49024
Agrachev, A. A.; Pallaschke, D.; Scholtes, S.
8
1997
Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023
Agrachev, A. A.; Sarychev, A. V.
39
1996
Exponential mappings for contact sub-Riemannian structures. Zbl 0941.53022
Agrachev, A. A.
35
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
3
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.
9
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.
5
1994
Local controllability and semigroups of diffeomorphisms. Zbl 0787.93010
Agrachev, A. A.; Gamkrelidze, R. V.
7
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
Symplectic geometry and necessary optimality conditions. Zbl 0729.49018
Agrachev, A. A.; Gamkrelidze, R. V.
9
1991
Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0727.58009
Agrachev, A. A.; Gamkrelidze, R. V.
6
1991
Newton diagrams and tangent cones to attainable sets. Zbl 0811.93006
Agrachev, A. A.
6
1991
Morse theory and optimal control problems. Zbl 0743.58008
Agrachev, A. A.; Vakhrameev, S. A.
4
1991
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
...and 27 more Documents
all top 5

Cited by 1,079 Authors

62 Agrachev, Andreĭ Aleksandrovich
54 Sachkov, Yuriĭ Leonidovich
38 Boscain, Ugo
25 Trélat, Emmanuel
23 Barilari, Davide
22 Sigalotti, Mario
19 Bonnard, Bernard
18 Le Donne, Enrico
17 Rizzi, Luca
15 Zelenko, Igor
14 Ardentov, Andrei A.
14 Arutyunov, Aram Vladimirovic
14 Gamkrelidze, Revaz Valerianovich
14 Gauthier, Jean-Paul A.
13 Biggs, Rory
13 Prandi, Dario
13 Remsing, Claudiu-Cristian
12 Chitour, Yacine
11 Caillau, Jean-Baptiste
11 Grong, Erlend
11 Nersesyan, Vahagn
11 Sachkova, Elena F.
11 Vakhrameev, S. A.
10 Berestovskiĭ, Valeriĭ Nikolaevich
10 Duits, Remco
10 Ebrahimi-Fard, Kurusch
10 Lee, Paul W. Y.
10 Rifford, Ludovic
9 Boarotto, Francesco
9 Chittaro, Francesca C.
9 Jean, Frédéric
9 Lokutsievskiy, Lev Viacheslavovich
9 Mason, Paolo
9 Podobryaev, Alekseĭ V.
9 Poggiolini, Laura
9 Shirikyan, Armen R.
8 Baudoin, Fabrice
8 Charlot, Grégoire
8 Godoy Molina, Mauricio
8 Ignatovich, Svetlana Yu.
8 Lerario, Antonio
8 Manchon, Dominique
8 Mashtakov, Alexey P.
8 Rossi, Francesco
7 Beschastnyi, Ivan Yu.
7 Caponigro, Marco
7 Grochowski, Marek
7 Kokkonen, Petri
7 Margaliot, Michael
7 Markina, Irina
7 Serres, Ulysse
7 Silva Leite, Fátima
6 Bauer, Wolfram
6 Ghezzi, Roberta
6 Karmanova, Maria B.
6 Khimshiashvili, Giorgi
6 Krasnov, Vyacheslav Alekseevich
6 Laurent, Camille
6 Li, Chengbo
6 Mamaev, Ivan Sergeevich
6 Neel, Robert Weston
6 Ottazzi, Alessandro
6 Patras, Frédéric
6 Shcherbakova, Nataliya
6 Sklyar, Grigory Mikhailovitch
6 Stefani, Gianna
6 Tryamkin, Maksim Vladimirovich
6 Vallarino, Maria
6 Vittone, Davide
6 Zakalyukin, Vladimir M.
5 Barbero-Liñán, María
5 Barrett, Dennis I.
5 Cannarsa, Piermarco
5 Chambrion, Thomas
5 Chyba, Monique
5 Doubrov, Boris M.
5 Furutani, Kenro
5 Gordina, Maria
5 Gupta, Rohit
5 Jouan, Philippe
5 Kilin, Aleksandr Aleksandrovich
5 Pelletier, Fernand
5 Schättler, Heinz Michael
5 Slyn’ko, Vitalii Ivanovich
5 Speight, Gareth
5 Zubareva, Irina Aleksandrovna
4 Albano, Paolo
4 Augier, Nicolas
4 Balogh, Zoltán M.
4 Beauchard, Karine
4 Bekkers, Erik J.
4 Bloch, Anthony Michael
4 Borisov, Alekseĭ Vladimirovich
4 Bruno, Tommaso
4 Cheng, Chun-Ming
4 Cheng, Daizhan
4 Chiou, Juing-Shian
4 Citti, Giovanna
4 Coron, Jean-Michel
4 Deng, Li
...and 979 more Authors
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Cited in 254 Serials

103 Journal of Dynamical and Control Systems
49 Journal of Mathematical Sciences (New York)
45 SIAM Journal on Control and Optimization
44 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
29 Systems & Control Letters
26 Automatica
23 Proceedings of the Steklov Institute of Mathematics
22 Journal of Differential Equations
20 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
19 Doklady Mathematics
18 Journal of Geometry and Physics
18 Siberian Mathematical Journal
18 Acta Applicandae Mathematicae
18 Differential Equations
17 Mathematical Notes
17 Journal of Optimization Theory and Applications
15 Differential Geometry and its Applications
15 The Journal of Geometric Analysis
15 Automation and Remote Control
15 Calculus of Variations and Partial Differential Equations
12 Journal of Soviet Mathematics
12 Regular and Chaotic Dynamics
11 Journal of Mathematical Analysis and Applications
11 Journal de Mathématiques Pures et Appliquées. Neuvième Série
11 Journal of Geometric Mechanics
9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
9 Transactions of the American Mathematical Society
9 MCSS. Mathematics of Control, Signals, and Systems
9 Potential Analysis
8 International Journal of Control
8 Journal of Mathematical Physics
8 Journal of Functional Analysis
8 Mathematische Zeitschrift
8 Discrete and Continuous Dynamical Systems
8 Comptes Rendus. Mathématique. Académie des Sciences, Paris
8 Mathematical Control and Related Fields
7 Annali di Matematica Pura ed Applicata. Serie Quarta
7 Sbornik: Mathematics
7 Journal of the European Mathematical Society (JEMS)
6 Communications in Mathematical Physics
6 Journal of Mathematical Imaging and Vision
6 Journal of Nonlinear Science
6 European Journal of Control
6 Russian Journal of Nonlinear Dynamics
5 Journal of the Franklin Institute
5 Advances in Mathematics
5 Annales de l’Institut Fourier
5 Journal of Algebra
5 Geometric and Functional Analysis. GAFA
5 Foundations of Computational Mathematics
5 Nonlinear Analysis. Hybrid Systems
5 Analysis and Geometry in Metric Spaces
4 Nonlinearity
4 Mathematische Annalen
4 Optimization
4 Discrete & Computational Geometry
4 Revista Matemática Iberoamericana
4 Computational Mathematics and Mathematical Physics
4 Linear Algebra and its Applications
4 Russian Mathematics
4 Abstract and Applied Analysis
4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
4 Analysis and Mathematical Physics
4 Nonlinear Analysis. Theory, Methods & Applications
4 European Journal of Mathematics
4 Séminaire Laurent Schwartz. EDP et Applications
3 Communications in Algebra
3 Journal of Applied Mathematics and Mechanics
3 Applied Mathematics and Computation
3 Inventiones Mathematicae
3 Mathematics and Computers in Simulation
3 Proceedings of the American Mathematical Society
3 Journal of Global Optimization
3 Communications in Partial Differential Equations
3 Stochastic Processes and their Applications
3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
3 Journal of Computer and Systems Sciences International
3 NoDEA. Nonlinear Differential Equations and Applications
3 Bulletin des Sciences Mathématiques
3 Electronic Journal of Probability
3 Izvestiya: Mathematics
3 Mathematical Problems in Engineering
3 Discrete and Continuous Dynamical Systems. Series B
3 Journal of Algebra and its Applications
3 International Journal of Geometric Methods in Modern Physics
3 Advances in Mathematical Physics
3 Journal de l’École Polytechnique – Mathématiques
3 Mechanics of Solids
2 Archive for Rational Mechanics and Analysis
2 International Journal of Systems Science
2 Israel Journal of Mathematics
2 Journal d’Analyse Mathématique
2 Journal of Mathematical Biology
2 Letters in Mathematical Physics
2 Reports on Mathematical Physics
2 Russian Mathematical Surveys
2 Theoretical and Mathematical Physics
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Reviews in Mathematical Physics
2 Chaos, Solitons and Fractals
...and 154 more Serials
all top 5

Cited in 58 Fields

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

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