Edit Profile (opens in new tab) Agrachev, Andreĭ Aleksandrovich Co-Author Distance Author ID: agrachev.andrej-a 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. more...less Further Spellings: Аграчев Андрей Александрович Homepage: http://people.sissa.it/~agrachev/ External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · GND · IdRef · theses.fr Documents Indexed: 156 Publications since 1975, including 4 Books and 6 Additional arXiv Preprints 4 Contributions as Editor Biographic References: 1 Publication Co-Authors: 100 Co-Authors with 121 Joint Publications 3,086 Co-Co-Authors all top 5 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 Sarychev, Andrey V. 5 Rizzi, Luca 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 Baryshnikov, Yuliy M. 2 Boarotto, Francesco 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 Baranzini, Stefano 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 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 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 1 Zarodov, V. R. 1 Zelikin, Mikhail Il’ich 1 Zhizhchenko, Alexey B. all top 5 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 all top 5 Fields 65 Calculus of variations and optimal control; optimization (49-XX) 59 Differential geometry (53-XX) 57 Systems theory; control (93-XX) 45 Global analysis, analysis on manifolds (58-XX) 24 Dynamical systems and ergodic theory (37-XX) 9 Partial differential equations (35-XX) 8 Ordinary differential equations (34-XX) 7 Topological groups, Lie groups (22-XX) 7 Manifolds and cell complexes (57-XX) 7 Mechanics of particles and systems (70-XX) 5 History and biography (01-XX) 5 Nonassociative rings and algebras (17-XX) 5 Functional analysis (46-XX) 4 General and overarching topics; collections (00-XX) 3 Algebraic geometry (14-XX) 3 Algebraic topology (55-XX) 3 Fluid mechanics (76-XX) 3 Operations research, mathematical programming (90-XX) 2 Group theory and generalizations (20-XX) 2 Real functions (26-XX) 2 Probability theory and stochastic processes (60-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 131 Publications have been cited 2,516 times in 1,342 Documents Cited by ▼ Year ▼ Control theory from the geometric viewpoint. Zbl 1062.93001 Agrachev, Andrei A.; Sachkov, Yuri L. 496 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 130 2020 Lie-algebraic stability criteria for switched systems. Zbl 0995.93064 Agrachev, Andrei A.; Liberzon, Daniel 87 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 67 2009 Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039 Agrachev, A.; Barilari, D. 52 2012 Exponential representation of flows and chronological calculus. Zbl 0408.34044 Agrachev, A. A.; Gamkrelidze, R. V. 49 1978 On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030 Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 49 2012 Chronological algebras and nonstationary vector fields. Zbl 0473.58021 Agrachev, A. A.; Gamkrelidze, R. V. 48 1980 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. 45 2004 Feedback-invariant optimal control theory and differential geometry. I: Regular extremals. Zbl 0952.49019 Agrachev, A. A.; Gamkrelidze, R. V. 44 1997 Strong optimality for a bang-bang trajectory. Zbl 1020.49021 Agrachev, Andrei A.; Stefani, Gianna; Zezza, Pierluigi 43 2002 Local invariants of smooth control systems. Zbl 0681.49018 Agrachev, A. A.; Gamkrelidze, R. V.; Sarychev, A. V. 43 1989 A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Zbl 1198.49041 Agrachev, Andrei; Boscain, Ugo; Sigalotti, Mario 43 2008 Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023 Agrachev, A. A.; Sarychev, A. V. 42 1996 Geometry of Jacobi curves. I. Zbl 1019.53038 Agrachev, A. A.; Zelenko, I. 39 2002 Exponential mappings for contact sub-Riemannian structures. Zbl 0941.53022 Agrachev, A. A. 39 1996 Sub-Riemannian sphere in Martinet flat case. Zbl 0902.53033 Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I. 37 1997 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. 29 2009 Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035 Agrachev, A. A. 28 2008 Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Zbl 1327.53032 Agrachev, Andrei; Lee, Paul W. Y. 26 2014 Curvature: a variational approach. Zbl 1409.49001 Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca 25 2018 Sub-Riemannian curvature in contact geometry. Zbl 1376.53059 Agrachev, Andrei; Barilari, Davide; Rizzi, Luca 25 2017 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 On the local structure of optimal trajectories in R\(^{3}\). Zbl 1057.49027 Agrachev, Andrei A.; Sigalotti, Mario 23 2003 The exponential representation of flows and the chronological calculus. Zbl 0429.34044 Agrachev, A. A.; Gamkrelidze, R. V. 23 1979 Symplectic geometry for optimal control. Zbl 0719.49023 Agrachev, A. A.; Gamkrelidze, R. V. 23 1990 Compactness for sub-Riemannian length–minimizers and subanalyticity. Zbl 1039.53038 Agrachev, A. 22 1998 Some open problems. Zbl 1292.49040 Agrachev, Andrei A. 20 2014 Rolling balls and octonions. Zbl 1153.70010 Agrachev, A. A. 20 2007 Filtrations of a Lie algebra of vector fields and nilpoint approximation of controlled systems. Zbl 0850.93106 Agrachev, A. A.; Sarychev, A. V. 19 1987 On abnormal extremals for Lagrange variational problems. Zbl 0826.49012 Agrachev, A. A.; Sarychev, A. V. 19 1995 Geometry of Jacobi curves. II. Zbl 1045.53051 Agrachev, A. A.; Zelenko, I. 18 2002 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 Ensemble controllability by Lie algebraic methods. Zbl 1350.93014 Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey 16 2016 Strong minimality of abnormal geodesics for \(2\)-distributions. Zbl 0951.53029 Agrachëv, A. A.; Sarychev, A. V. 16 1995 On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014 Agrachev, Andrei; Gauthier, Jean-Paul 16 2001 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 Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Zbl 1068.58001 Agrachev, A.; Marigo, A. 15 2003 Solid controllability in fluid dynamics. Zbl 1141.76026 Agrachev, Andrey; Sarychev, Andrey 15 2008 Systems of quadratic inequalities. Zbl 1277.14046 Agrachev, A.; Lerario, A. 15 2012 Topology of quadratic maps and Hessians of smooth maps. Zbl 0719.58006 Agrachev, A. A. 15 1990 Homology of intersections of real quadrics. Zbl 0696.55004 Agrachev, A. A. 14 1988 A second order optimality principle for a time-optimal problem. Zbl 0377.49014 Agrachev, A. A.; Gamkrelidze, R. V. 14 1978 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 Sub-Riemannian metrics: Minimality of abnormal geodesics versus subanalyticity. Zbl 0978.53065 Agrachev, Andrei A.; Sarychev, Andrei V. 12 1999 On robust Lie-algebraic stability conditions for switched linear systems. Zbl 1238.93092 Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel 12 2012 Ordinary differential equations on vector bundles and chronological calculi. Zbl 0719.58033 Agrachev, A. A.; Gamkrelidze, R. V.; Vakhrameev, S. A. 12 1989 An invariant second variation in optimal control. Zbl 0945.49015 Agrachev, A.; Stefani, G.; Zezza, P. 11 1998 Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043 Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio 11 2015 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 Quadratic mappings in geometric control theory. Zbl 1267.93035 Agrachev, A. A. 11 1990 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 10 2020 On Morse theory for piecewise smooth functions. Zbl 0951.49024 Agrachev, A. A.; Pallaschke, D.; Scholtes, S. 10 1997 Local controllability and semigroups of diffeomorphisms. Zbl 0787.93010 Agrachev, A. A.; Gamkrelidze, R. V. 10 1993 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 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 Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0719.58013 Agrachev, A. A.; Gamkrelidze, R. V. 10 1989 Symplectic geometry and necessary optimality conditions. Zbl 0729.49018 Agrachev, A. A.; Gamkrelidze, R. V. 9 1991 On the Dido problem and plane isoperimetric problems. Zbl 0977.53068 Agrachev, Andrei A.; Gauthier, Jean-Paul A. 8 1999 Switching in time-optimal problem with control in a ball. Zbl 1386.49001 Agrachev, Andrei A.; Biolo, Carolina 8 2018 On conjugate times of LQ optimal control problems. Zbl 1378.49034 Agrachev, Andrei; Rizzi, Luca; Silveira, Pavel 8 2015 On the space of symmetric operators with multiple ground states. Zbl 1271.46056 Agrachev, A. A. 8 2011 Computation of the Euler characteristic of intersections of real quadrics. Zbl 0721.55001 Agrachev, A. A.; Gamkrelidze, R. V. 8 1988 On feedback classification of control-affine systems with one- and two-dimensional inputs. Zbl 1140.93018 Agrachev, Andrei; Zelenko, Igor 8 2007 Chebyshev polynomials and best rank-one approximation ratio. Zbl 1435.15019 Agrachev, Andrei; Kozhasov, Khazhgali; Uschmajew, André 7 2020 The control of rotation for asymmetric rigid body. Zbl 0571.70030 Agrachev, A. A.; Sarychev, A. V. 7 1983 The index of extremality and quasiextremal controls. Zbl 0587.49018 Agrachev, A. A.; Gamkrelidze, R. V. 7 1985 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 Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0727.58009 Agrachev, A. A.; Gamkrelidze, R. V. 7 1991 Switching in time-optimal problem: the 3D case with 2D control. Zbl 1379.49006 Agrachev, Andrei A.; Biolo, Carolina 7 2017 Local controllability for families of diffeomorphisms. Zbl 0778.93003 Agrachev, A. A.; Gamkrelidze, R. V. 6 1993 Topics in sub-Riemannian geometry. Zbl 1367.53028 Agrachev, A. A. 6 2016 Newton diagrams and tangent cones to attainable sets. Zbl 0811.93006 Agrachev, A. A. 6 1991 The shuffle product and symmetric groups. Zbl 0790.05095 Agrachev, A. A.; Gamkrelidze, R. V. 6 1994 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 Control on the manifolds of mappings with a view to the deep learning. Zbl 1498.93033 Agrachev, Andrei; Sarychev, Andrey 6 2022 Morse theory and optimal control problems. Zbl 0743.58008 Agrachev, A. A.; Vakhrameev, S. A. 5 1991 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 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 On reduction of a smooth system linear in the control. Zbl 0678.49034 Agrachev, A. A.; Sarychev, A. V. 5 1987 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 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 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 Symplectic geometry of constrained optimization. Zbl 1408.49043 Agrachev, Andrey A.; Beschastnyi, Ivan Yu. 4 2017 One more condition for a conditional extremum. Zbl 0693.49011 Agrachev, A. A. 4 1989 The Morse index and the Maslov index for extremals of controlled systems. Zbl 0614.58016 Agrachev, A. A.; Gamkrelidze, R. V. 4 1986 The geometry of maximum principle. Zbl 1227.49026 Agrachev, A. A.; Gamkrelidze, R. V. 4 2011 Continuity of optimal control costs and its application to weak KAM theory. Zbl 1203.49041 Agrachev, Andrei; Lee, Paul W. Y. 4 2010 Principal invariants of Jacobi curves. Zbl 1239.53059 Agrachev, Andrei; Zelenko, Igor 4 2001 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 3 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 130 2020 Control in the spaces of ensembles of points. Zbl 1447.93053 Agrachev, Andrei; Sarychev, Andrey 10 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. 1 2019 Curvature: a variational approach. Zbl 1409.49001 Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca 25 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 25 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. 4 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 16 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 Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043 Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio 11 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 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. 20 2014 Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039 Agrachev, A.; Barilari, D. 52 2012 On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030 Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 49 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. 8 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 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 Well-posed infinite horizon variational problems on a compact manifold. Zbl 1204.58012 Agrachev, A. A. 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 67 2009 Any sub-Riemannian metric has points of smoothness. Zbl 1253.53029 Agrachev, A. A. 29 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 43 2008 Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035 Agrachev, A. A. 28 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. 496 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. 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 87 2001 On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014 Agrachev, Andrei; Gauthier, Jean-Paul 16 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. 12 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. 1 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. 11 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. 37 1997 On Morse theory for piecewise smooth functions. Zbl 0951.49024 Agrachev, A. A.; Pallaschke, D.; Scholtes, S. 10 1997 Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023 Agrachev, A. A.; Sarychev, A. V. 42 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. 6 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 Symplectic geometry and necessary optimality conditions. Zbl 0729.49018 Agrachev, A. A.; Gamkrelidze, R. V. 9 1991 ...and 31 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,253 Authors 65 Agrachev, Andreĭ Aleksandrovich 62 Sachkov, Yuriĭ Leonidovich 40 Boscain, Ugo 28 Trélat, Emmanuel 26 Barilari, Davide 24 Le Donne, Enrico 23 Sigalotti, Mario 20 Bonnard, Bernard 20 Rizzi, Luca 16 Chitour, Yacine 15 Arutyunov, Aram Vladimirovic 15 Zelenko, Igor 14 Gamkrelidze, Revaz Valerianovich 14 Gauthier, Jean-Paul A. 14 Grong, Erlend 14 Prandi, Dario 14 Sachkova, Elena F. 13 Biggs, Rory 13 Mashtakov, Alexey P. 13 Remsing, Claudiu-Cristian 12 Nersesyan, Vahagn 12 Poggiolini, Laura 11 Caillau, Jean-Baptiste 11 Chittaro, Francesca C. 11 Duits, Remco 11 Ebrahimi-Fard, Kurusch 11 Lokutsievskiy, Lev Viacheslavovich 11 Rifford, Ludovic 11 Vakhrameev, S. A. 10 Berestovskiĭ, Valeriĭ Nikolaevich 10 Beschastnyi, Ivan Yu. 10 Boarotto, Francesco 10 Markina, Irina 10 Podobryaev, Alekseĭ V. 10 Silva Leite, Fátima 9 Baudoin, Fabrice 9 Grochowski, Marek 9 Jean, Frédéric 9 Kokkonen, Petri 9 Lerario, Antonio 9 Manchon, Dominique 9 Mason, Paolo 9 Shirikyan, Armen R. 8 Charlot, Grégoire 8 Godoy Molina, Mauricio 8 Ignatovich, Svetlana Yu. 8 Patras, Frédéric 8 Rossi, Francesco 8 Vittone, Davide 7 Caponigro, Marco 7 Krasnov, Vyacheslav Alekseevich 7 Margaliot, Michael 7 Pozzoli, Eugenio 7 Serres, Ulysse 7 Stefani, Gianna 7 Vallarino, Maria 6 Barbero-Liñán, María 6 Bauer, Wolfram 6 Bourdin, Loïc 6 Bruno, Tommaso 6 Chambrion, Thomas 6 Ghezzi, Roberta 6 Greshnov, Aleksandr Valer’evich 6 Jouan, Philippe 6 Khimshiashvili, Giorgi 6 Laurent, Camille 6 Lee, Paul W. Y. 6 Li, Chengbo 6 Mahmudov, Elimhan Nadir 6 Mamaev, Ivan Sergeevich 6 Neel, Robert Weston 6 Ottazzi, Alessandro 6 Pinamonti, Andrea 6 Shcherbakova, Nataliya 6 Sklyar, Grigory Mikhailovitch 6 Slyn’ko, Vitalii Ivanovich 6 Speight, Gareth 6 Tryamkin, Maksim Vladimirovich 6 Zakalyukin, Vladimir M. 5 Ardentov, Andrei A. 5 Augier, Nicolas 5 Ayala, Victor 5 Barrett, Dennis I. 5 Basu, Saugata 5 Beauchard, Karine 5 Cannarsa, Piermarco 5 Chyba, Monique 5 Coron, Jean-Michel 5 Deng, Li 5 Doubrov, Boris M. 5 Durán Fernandez, Carlos Eduardo 5 Furutani, Kenro 5 Gordina, Maria 5 Gupta, Rohit 5 Hakavuori, Eero 5 Hrdina, Jaroslav 5 Jurdjevic, Velimir 5 Kilin, Aleksandr Aleksandrovich 5 Kozhasov, Khazhgali 5 Léautaud, Matthieu ...and 1,153 more Authors all top 5 Cited in 290 Serials 123 Journal of Dynamical and Control Systems 53 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 32 Systems & Control Letters 30 Automatica 29 Proceedings of the Steklov Institute of Mathematics 28 Journal of Differential Equations 22 Journal of Geometry and Physics 21 Annales de l’Institut Henri Poincaré. 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Mathematics of Control, Signals, and Systems 9 Transactions of the American Mathematical Society 9 Discrete and Continuous Dynamical Systems 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 International Journal of Control 8 Mathematische Zeitschrift 8 Sbornik: Mathematics 8 Journal of the European Mathematical Society (JEMS) 7 Journal of the Franklin Institute 7 Nonlinearity 7 Advances in Mathematics 7 Journal of Nonlinear Science 7 Izvestiya: Mathematics 7 European Journal of Control 7 Journal of Physics A: Mathematical and Theoretical 6 Communications in Mathematical Physics 6 Discrete & Computational Geometry 6 Journal of Mathematical Imaging and Vision 6 Analysis and Geometry in Metric Spaces 6 Russian Journal of Nonlinear Dynamics 5 Annales de l’Institut Fourier 5 Applied Mathematics and Optimization 5 Journal of Algebra 5 Optimization 5 Geometric and Functional Analysis. GAFA 5 NoDEA. 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EDP et Applications 3 Communications in Algebra 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 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 Discrete and Continuous Dynamical Systems. Series B 3 SIAM Journal on Applied Dynamical Systems 3 International Journal of Geometric Methods in Modern Physics 3 Oberwolfach Reports 3 Advances in Mathematical Physics 3 Journal of Computational Dynamics 3 SIAM Journal on Applied Algebra and Geometry ...and 190 more Serials all top 5 Cited in 58 Fields 493 Differential geometry (53-XX) 452 Calculus of variations and optimal control; optimization (49-XX) 431 Systems theory; control (93-XX) 197 Global analysis, analysis on manifolds (58-XX) 176 Partial differential equations (35-XX) 122 Dynamical systems and ergodic theory (37-XX) 116 Ordinary differential equations (34-XX) 113 Topological groups, Lie groups (22-XX) 112 Mechanics of particles and systems (70-XX) 56 Quantum theory (81-XX) 50 Nonassociative rings and algebras (17-XX) 50 Fluid mechanics (76-XX) 49 Numerical analysis (65-XX) 42 Algebraic geometry (14-XX) 42 Probability theory and stochastic processes (60-XX) 37 Operations research, mathematical programming (90-XX) 33 Operator theory (47-XX) 32 Biology and other natural sciences (92-XX) 31 Abstract harmonic analysis (43-XX) 30 Manifolds and cell complexes (57-XX) 29 Real functions (26-XX) 28 Functional analysis (46-XX) 27 Measure and integration (28-XX) 20 Associative rings and algebras (16-XX) 20 Computer science (68-XX) 16 Several complex variables and analytic spaces (32-XX) 15 Combinatorics (05-XX) 15 Mechanics of deformable solids (74-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 12 Geometry (51-XX) 12 Information and communication theory, circuits (94-XX) 11 General topology (54-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Functions of a complex variable (30-XX) 9 Algebraic topology (55-XX) 8 Group theory and generalizations (20-XX) 7 Convex and discrete geometry (52-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 General and overarching topics; collections (00-XX) 5 Statistics (62-XX) 4 Category theory; homological algebra (18-XX) 4 Potential theory (31-XX) 4 Approximations and expansions (41-XX) 4 Integral equations (45-XX) 4 Optics, electromagnetic theory (78-XX) 3 Mathematical logic and foundations (03-XX) 3 Special functions (33-XX) 3 Difference and functional equations (39-XX) 3 Relativity and gravitational theory (83-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Commutative algebra (13-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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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