Edit Profile (opens in new tab) Agrachev, Andreĭ Aleksandrovich Compute Distance To: Compute 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: 148 Publications since 1975, including 4 Books 4 Contributions as Editor Biographic References: 1 Publication Co-Authors: 96 Co-Authors with 115 Joint Publications 2,847 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 all top 5 Fields 64 Calculus of variations and optimal control; optimization (49-XX) 57 Systems theory; control (93-XX) 56 Differential geometry (53-XX) 43 Global analysis, analysis on manifolds (58-XX) 23 Dynamical systems and ergodic theory (37-XX) 8 Ordinary differential equations (34-XX) 8 Partial differential equations (35-XX) 7 Mechanics of particles and systems (70-XX) 6 Topological groups, Lie groups (22-XX) 6 Manifolds and cell complexes (57-XX) 5 History and biography (01-XX) 5 Functional analysis (46-XX) 4 General and overarching topics; collections (00-XX) 4 Nonassociative rings and algebras (17-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 127 Publications have been cited 2,148 times in 1,153 Documents Cited by ▼ Year ▼ Control theory from the geometric viewpoint. Zbl 1062.93001Agrachev, Andrei A.; Sachkov, Yuri L. 389 2004 Lie-algebraic stability criteria for switched systems. Zbl 0995.93064Agrachev, Andrei A.; Liberzon, Daniel 82 2001 A comprehensive introduction to sub-Riemannian geometry. From the Hamiltonian viewpoint. With an appendix by Igor Zelenko. Zbl 1487.53001Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 74 2020 Introduction to geodesics in sub-Riemannian geometry. Zbl 1362.53001Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 66 2016 The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups. Zbl 1165.58012Agrachev, Andrei; Boscain, Ugo; Gauthier, Jean-Paul; Rossi, Francesco 61 2009 Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039Agrachev, A.; Barilari, D. 48 2012 Exponential representation of flows and chronological calculus. Zbl 0408.34044Agrachev, A. A.; Gamkrelidze, R. V. 47 1978 Feedback-invariant optimal control theory and differential geometry. I: Regular extremals. Zbl 0952.49019Agrachev, A. A.; Gamkrelidze, R. V. 45 1997 Geometric control theory. (Геометрическая теория управления.) Zbl 1078.93001Agrachev, A. A.; Sachkov, Yu. L. 45 2004 Chronological algebras and nonstationary vector fields. Zbl 0473.58021Agrachev, A. A.; Gamkrelidze, R. V. 45 1980 On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 44 2012 Local invariants of smooth control systems. Zbl 0681.49018Agrachev, A. A.; Gamkrelidze, R. V.; Sarychev, A. V. 44 1989 Navier-Stokes equations: controllability by means of low modes forcing. Zbl 1075.93014Agrachev, Andrey A.; Sarychev, Andrey V. 40 2005 Geometry of Jacobi curves. I. Zbl 1019.53038Agrachev, A. A.; Zelenko, I. 39 2002 Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023Agrachev, A. A.; Sarychev, A. V. 39 1996 Strong optimality for a bang-bang trajectory. Zbl 1020.49021Agrachev, Andrei A.; Stefani, Gianna; Zezza, Pierluigi 38 2002 A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Zbl 1198.49041Agrachev, Andrei; Boscain, Ugo; Sigalotti, Mario 35 2008 Exponential mappings for contact sub-Riemannian structures. Zbl 0941.53022Agrachev, A. A. 35 1996 Sub-Riemannian sphere in Martinet flat case. Zbl 0902.53033Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I. 34 1997 Any sub-Riemannian metric has points of smoothness. Zbl 1253.53029Agrachev, A. A. 27 2009 Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing. Zbl 1105.93008Agrachev, Andrey A.; Sarychev, Andrey V. 26 2006 Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Zbl 1327.53032Agrachev, Andrei; Lee, Paul W. Y. 24 2014 Sub-Riemannian curvature in contact geometry. Zbl 1376.53059Agrachev, Andrei; Barilari, Davide; Rizzi, Luca 24 2017 Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035Agrachev, A. A. 22 2008 Optimal transportation under nonholonomic constraints. Zbl 1175.49037Agrachev, Andrei; Lee, Paul 22 2009 On the local structure of optimal trajectories in R\(^{3}\). Zbl 1057.49027Agrachev, Andrei A.; Sigalotti, Mario 22 2003 The exponential representation of flows and the chronological calculus. Zbl 0429.34044Agrachev, A. A.; Gamkrelidze, R. V. 21 1979 Two-dimensional almost-Riemannian structures with tangency points. Zbl 1192.53029Agrachev, A. A.; Boscain, U.; Charlot, G.; Ghezzi, R.; Sigalotti, M. 19 2010 Rolling balls and octonions. Zbl 1153.70010Agrachev, A. A. 19 2007 On abnormal extremals for Lagrange variational problems. Zbl 0826.49012Agrachev, A. A.; Sarychev, A. V. 19 1995 Compactness for sub-Riemannian length–minimizers and subanalyticity. Zbl 1039.53038Agrachev, A. 18 1998 Geometry of Jacobi curves. II. Zbl 1045.53051Agrachev, A. A.; Zelenko, I. 17 2002 On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Zbl 1177.60059Agrachev, A.; Kuksin, S.; Sarychev, A.; Shirikyan, A. 16 2007 Filtrations of a Lie algebra of vector fields and nilpoint approximation of controlled systems. Zbl 0850.93106Agrachev, A. A.; Sarychev, A. V. 16 1987 Curvature: a variational approach. Zbl 1409.49001Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca 16 2018 Symplectic geometry for optimal control. Zbl 0719.49023Agrachev, A. A.; Gamkrelidze, R. V. 16 1990 Strong minimality of abnormal geodesics for \(2\)-distributions. Zbl 0951.53029Agrachëv, A. A.; Sarychev, A. V. 16 1995 Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals. Zbl 0972.49014Agrachev, A. A. 16 1998 Some open problems. Zbl 1292.49040Agrachev, Andrei A. 15 2014 Sub-Riemannian metrics on \(\mathbb{R}^3\). Zbl 0962.53022Agrachev, A. A.; Chakir El-A., El-H.; Gauthier, J. P. 15 1998 On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014Agrachev, Andrei; Gauthier, Jean-Paul 14 2001 A second order optimality principle for a time-optimal problem. Zbl 0377.49014Agrachev, A. A.; Gamkrelidze, R. V. 14 1978 Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Zbl 1068.58001Agrachev, A.; Marigo, A. 14 2003 Solid controllability in fluid dynamics. Zbl 1141.76026Agrachev, Andrey; Sarychev, Andrey 13 2008 Systems of quadratic inequalities. Zbl 1277.14046Agrachev, A.; Lerario, A. 12 2012 On robust Lie-algebraic stability conditions for switched linear systems. Zbl 1238.93092Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel 12 2012 Symplectic methods for optimization and control. Zbl 0965.93034Agrachev, A.; Gamkrelidze, R. 12 1998 An estimation of the controllability time for single-input systems on compact Lie groups. Zbl 1106.93006Agrachev, Andrei; Chambrion, Thomas 11 2006 Ordinary differential equations on vector bundles and chronological calculi. Zbl 0719.58033Agrachev, A. A.; Gamkrelidze, R. V.; Vakhrameev, S. A. 11 1989 Homology of intersections of real quadrics. Zbl 0696.55004Agrachev, A. A. 11 1988 Differential-geometric and group-theoretic methods in the theory of optimal control. Zbl 0542.93045Agrachev, A. A.; Vakhrameev, S. A.; Gamkrelidze, R. V. 11 1983 Ensemble controllability by Lie algebraic methods. Zbl 1350.93014Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey 11 2016 Bishop and Laplacian comparison theorems on three-dimensional contact sub-Riemannian manifolds with symmetry. Zbl 1341.53058Agrachev, Andrei; Lee, Paul W. Y. 10 2015 Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio 10 2015 Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0719.58013Agrachev, A. A.; Gamkrelidze, R. V. 10 1989 Sub-Riemannian metrics: Minimality of abnormal geodesics versus subanalyticity. Zbl 0978.53065Agrachev, Andrei A.; Sarychev, Andrei V. 10 1999 Methods of control theory in nonholonomic geometry. Zbl 0848.93012Agrachev, Andrej A. 9 1995 Controllability on the group of diffeomorphisms. Zbl 1188.93016Agrachev, A. A.; Caponigro, M. 9 2009 Symplectic geometry and necessary optimality conditions. Zbl 0729.49018Agrachev, A. A.; Gamkrelidze, R. V. 9 1991 Rigid Carnot algebras: a classification. Zbl 1125.17002Agrachev, A.; Marigo, A. 9 2005 On feedback classification of control-affine systems with one- and two-dimensional inputs. Zbl 1140.93018Agrachev, Andrei; Zelenko, Igor 8 2007 Topology of quadratic maps and Hessians of smooth maps. Zbl 0719.58006Agrachev, A. A. 8 1990 Computation of the Euler characteristic of intersections of real quadrics. Zbl 0721.55001Agrachev, A. A.; Gamkrelidze, R. V. 8 1988 Quadratic mappings in geometric control theory. Zbl 1267.93035Agrachev, A. A. 8 1990 On Morse theory for piecewise smooth functions. Zbl 0951.49024Agrachev, A. A.; Pallaschke, D.; Scholtes, S. 8 1997 An invariant second variation in optimal control. Zbl 0945.49015Agrachev, A.; Stefani, G.; Zezza, P. 8 1998 Control in the spaces of ensembles of points. Zbl 1447.93053Agrachev, Andrei; Sarychev, Andrey 7 2020 On the space of symmetric operators with multiple ground states. Zbl 1271.46056Agrachev, A. A. 7 2011 Switching in time-optimal problem with control in a ball. Zbl 1386.49001Agrachev, Andrei A.; Biolo, Carolina 7 2018 Switching in time-optimal problem: the 3D case with 2D control. Zbl 1379.49006Agrachev, Andrei A.; Biolo, Carolina 7 2017 The index of extremality and quasiextremal controls. Zbl 0587.49018Agrachev, A. A.; Gamkrelidze, R. V. 7 1985 On sub-Riemann caustics and wave fronts for contact distributions in the three-space. Zbl 1040.58017Agrachev, A. A.; Charlot, G.; Gauthier, J. P. A.; Zakalyukin, V. M. 7 2000 The control of rotation for asymmetric rigid body. Zbl 0571.70030Agrachev, A. A.; Sarychev, A. V. 7 1983 Local controllability and semigroups of diffeomorphisms. Zbl 0787.93010Agrachev, A. A.; Gamkrelidze, R. V. 7 1993 On the Dido problem and plane isoperimetric problems. Zbl 0977.53068Agrachev, Andrei A.; Gauthier, Jean-Paul A. 7 1999 On conjugate times of LQ optimal control problems. Zbl 1378.49034Agrachev, Andrei; Rizzi, Luca; Silveira, Pavel 7 2015 Local controllability for families of diffeomorphisms. Zbl 0778.93003Agrachev, A. A.; Gamkrelidze, R. V. 6 1993 Newton diagrams and tangent cones to attainable sets. Zbl 0811.93006Agrachev, A. A. 6 1991 Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0727.58009Agrachev, A. A.; Gamkrelidze, R. V. 6 1991 On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals. Zbl 1160.37383Agrachev, A. A.; Chtcherbakova, N. N.; Zelenko, I. 6 2005 A second-order necessary condition for optimality in the general nonlinear case. Zbl 0386.49012Agrachev, A. A. 6 1977 On regularity properties of extremal controls. Zbl 0951.49004Agrachëv, A. A. 5 1995 The shuffle product and symmetric groups. Zbl 0790.05095Agrachev, A. A.; Gamkrelidze, R. V. 5 1994 Sub-Riemannian metrics and isoperimetric problems in the contact case. Zbl 1008.53019Agrachev, A. A.; Gauthier, J. P. A. 5 2001 A Hamiltonian approach to strong minima in optimal control. Zbl 0937.49012Agrachev, Andrei; Stefani, Gianna; Zezza, Pierluigi 5 1999 Topics in sub-Riemannian geometry. Zbl 1367.53028Agrachev, A. A. 5 2016 Morse theory and optimal control problems. Zbl 0743.58008Agrachev, A. A.; Vakhrameev, S. A. 4 1991 Principal invariants of Jacobi curves. Zbl 1239.53059Agrachev, Andrei; Zelenko, Igor 4 2001 Homotopically invisible singular curves. Zbl 1377.53048Agrachev, Andrei A.; Boarotto, Francesco; Lerario, Antonio 4 2017 One more condition for a conditional extremum. Zbl 0693.49011Agrachev, A. A. 4 1989 Level set for a smooth mapping in the neighborhood of a singular point and zeros of a quadratic mapping. Zbl 0762.46028Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V. 4 1991 The Morse index and the Maslov index for extremals of controlled systems. Zbl 0614.58016Agrachev, A. A.; Gamkrelidze, R. V. 4 1986 Chronological series and the Cauchy-Kovalevskaya theorem. Zbl 0485.35004Agrachev, A. A.; Vakhrameev, S. A. 4 1981 Continuity of optimal control costs and its application to weak KAM theory. Zbl 1203.49041Agrachev, Andrei; Lee, Paul W. Y. 3 2010 The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping. Zbl 0772.46021Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V. 3 1992 Generic singularities of sub-Riemannian metrics on \(\mathbb{R}^ 3\). Zbl 0843.53025Agrachev, Andrei; El Alaoui, El-Houcine Chakir; Gauthier, Jean-Paul; Kupka, Ivan 3 1996 The Pontryagin maximum principle 50 years later. Zbl 1122.49001Agrachev, A. A.; Gamkrelidze, R. V. 3 2006 The geometry of maximum principle. Zbl 1227.49026Agrachev, A. A.; Gamkrelidze, R. V. 3 2011 Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling. Zbl 1481.53041Agrachev, Andrei; Boscain, Ugo; Neel, Robert; Rizzi, Luca 3 2018 Quasi-extremality for control systems. Zbl 0721.58014Agrachev, A. A.; Gamkrelidze, R. V. 3 1989 A comprehensive introduction to sub-Riemannian geometry. From the Hamiltonian viewpoint. With an appendix by Igor Zelenko. Zbl 1487.53001Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 74 2020 Control in the spaces of ensembles of points. Zbl 1447.93053Agrachev, Andrei; Sarychev, Andrey 7 2020 Chebyshev polynomials and best rank-one approximation ratio. Zbl 1435.15019Agrachev, Andrei; Kozhasov, Khazhgali; Uschmajew, André 2 2020 Jacobi fields in optimal control: one-dimensional variations. Zbl 1451.49003Agrachev, 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 1421.53037Agrachev, Andrei A.; Barilari, Davide; Paoli, Elisa 3 2019 Optimality of broken extremals. Zbl 1419.49013Agrachev, Andrei A.; Biolo, Carolina 3 2019 Curvature: a variational approach. Zbl 1409.49001Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca 16 2018 Switching in time-optimal problem with control in a ball. Zbl 1386.49001Agrachev, Andrei A.; Biolo, Carolina 7 2018 Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling. Zbl 1481.53041Agrachev, Andrei; Boscain, Ugo; Neel, Robert; Rizzi, Luca 3 2018 Sub-Riemannian curvature in contact geometry. Zbl 1376.53059Agrachev, Andrei; Barilari, Davide; Rizzi, Luca 24 2017 Switching in time-optimal problem: the 3D case with 2D control. Zbl 1379.49006Agrachev, Andrei A.; Biolo, Carolina 7 2017 Homotopically invisible singular curves. Zbl 1377.53048Agrachev, Andrei A.; Boarotto, Francesco; Lerario, Antonio 4 2017 Symplectic geometry of constrained optimization. Zbl 1408.49043Agrachev, Andrey A.; Beschastnyi, Ivan Yu. 2 2017 Introduction to geodesics in sub-Riemannian geometry. Zbl 1362.53001Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 66 2016 Ensemble controllability by Lie algebraic methods. Zbl 1350.93014Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey 11 2016 Topics in sub-Riemannian geometry. Zbl 1367.53028Agrachev, A. A. 5 2016 Tangent hyperplanes to Subriemannian balls. Zbl 1351.53049Agrachev, A. A. 1 2016 Bishop and Laplacian comparison theorems on three-dimensional contact sub-Riemannian manifolds with symmetry. Zbl 1341.53058Agrachev, Andrei; Lee, Paul W. Y. 10 2015 Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio 10 2015 On conjugate times of LQ optimal control problems. Zbl 1378.49034Agrachev, Andrei; Rizzi, Luca; Silveira, Pavel 7 2015 Quadratic cohomology. Zbl 1331.55003Agrachev, A. A. 2 2015 Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Zbl 1327.53032Agrachev, Andrei; Lee, Paul W. Y. 24 2014 Some open problems. Zbl 1292.49040Agrachev, Andrei A. 15 2014 Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039Agrachev, A.; Barilari, D. 48 2012 On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 44 2012 Systems of quadratic inequalities. Zbl 1277.14046Agrachev, A.; Lerario, A. 12 2012 On robust Lie-algebraic stability conditions for switched linear systems. Zbl 1238.93092Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel 12 2012 On the space of symmetric operators with multiple ground states. Zbl 1271.46056Agrachev, A. A. 7 2011 The geometry of maximum principle. Zbl 1227.49026Agrachev, A. A.; Gamkrelidze, R. V. 3 2011 Two-dimensional almost-Riemannian structures with tangency points. Zbl 1192.53029Agrachev, 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 1203.49041Agrachev, Andrei; Lee, Paul W. Y. 3 2010 Dynamics control by a time-varying feedback. Zbl 1203.93046Agrachev, A. A.; Caponigro, M. 2 2010 Invariant Lagrangian submanifolds of dissipative systems. Zbl 1233.37030Agrachev, A. A. 2 2010 In memory of Evgenii Frolovich Mishchenko. Zbl 1302.01048Osipov, 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 1165.58012Agrachev, Andrei; Boscain, Ugo; Gauthier, Jean-Paul; Rossi, Francesco 61 2009 Any sub-Riemannian metric has points of smoothness. Zbl 1253.53029Agrachev, A. A. 27 2009 Optimal transportation under nonholonomic constraints. Zbl 1175.49037Agrachev, Andrei; Lee, Paul 22 2009 Controllability on the group of diffeomorphisms. Zbl 1188.93016Agrachev, A. A.; Caponigro, M. 9 2009 Smooth optimal synthesis for infinite horizon variational problems. Zbl 1158.49039Agrachev, Andrei A.; Chittaro, Francesca C. 2 2009 A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Zbl 1198.49041Agrachev, Andrei; Boscain, Ugo; Sigalotti, Mario 35 2008 Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035Agrachev, A. A. 22 2008 Solid controllability in fluid dynamics. Zbl 1141.76026Agrachev, Andrey; Sarychev, Andrey 13 2008 Rolling balls and octonions. Zbl 1153.70010Agrachev, A. A. 19 2007 On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Zbl 1177.60059Agrachev, A.; Kuksin, S.; Sarychev, A.; Shirikyan, A. 16 2007 On feedback classification of control-affine systems with one- and two-dimensional inputs. Zbl 1140.93018Agrachev, Andrei; Zelenko, Igor 8 2007 The curvature and hyperbolicity of Hamiltonian systems. Zbl 1153.37346Agrachev, A. A. 1 2007 Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing. Zbl 1105.93008Agrachev, Andrey A.; Sarychev, Andrey V. 26 2006 An estimation of the controllability time for single-input systems on compact Lie groups. Zbl 1106.93006Agrachev, Andrei; Chambrion, Thomas 11 2006 The Pontryagin maximum principle 50 years later. Zbl 1122.49001Agrachev, A. A.; Gamkrelidze, R. V. 3 2006 Vector fields on \(n\)-foliated \(2n\)-dimensional manifolds. Zbl 1244.53094Agrachev, A. A.; Gamkrelidze, R. V. 1 2006 Navier-Stokes equations: controllability by means of low modes forcing. Zbl 1075.93014Agrachev, Andrey A.; Sarychev, Andrey V. 40 2005 Rigid Carnot algebras: a classification. Zbl 1125.17002Agrachev, A.; Marigo, A. 9 2005 On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals. Zbl 1160.37383Agrachev, A. A.; Chtcherbakova, N. N.; Zelenko, I. 6 2005 Control theory from the geometric viewpoint. Zbl 1062.93001Agrachev, Andrei A.; Sachkov, Yuri L. 389 2004 Geometric control theory. (Геометрическая теория управления.) Zbl 1078.93001Agrachev, A. A.; Sachkov, Yu. L. 45 2004 Controllability of the Navier-Stokes equation by few low modes forcing. Zbl 1123.93020Agrachev, A. A.; Sarychev, A. V. 2 2004 On the local structure of optimal trajectories in R\(^{3}\). Zbl 1057.49027Agrachev, Andrei A.; Sigalotti, Mario 22 2003 Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Zbl 1068.58001Agrachev, A.; Marigo, A. 14 2003 Geometry of Jacobi curves. I. Zbl 1019.53038Agrachev, A. A.; Zelenko, I. 39 2002 Strong optimality for a bang-bang trajectory. Zbl 1020.49021Agrachev, Andrei A.; Stefani, Gianna; Zezza, Pierluigi 38 2002 Geometry of Jacobi curves. II. Zbl 1045.53051Agrachev, A. A.; Zelenko, I. 17 2002 Introduction to optimal control theory. Zbl 1034.93010Agrachev, Andrei A. 1 2002 Lie-algebraic stability criteria for switched systems. Zbl 0995.93064Agrachev, Andrei A.; Liberzon, Daniel 82 2001 On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014Agrachev, Andrei; Gauthier, Jean-Paul 14 2001 Sub-Riemannian metrics and isoperimetric problems in the contact case. Zbl 1008.53019Agrachev, A. A.; Gauthier, J. P. A. 5 2001 Principal invariants of Jacobi curves. Zbl 1239.53059Agrachev, Andrei; Zelenko, Igor 4 2001 A “Gauss-Bonnet formula” for contact sub-Riemannian manifolds. Zbl 1044.53021Agrachev, A. A. 3 2001 On sub-Riemann caustics and wave fronts for contact distributions in the three-space. Zbl 1040.58017Agrachev, A. A.; Charlot, G.; Gauthier, J. P. A.; Zakalyukin, V. M. 7 2000 Sub-Riemannian metrics: Minimality of abnormal geodesics versus subanalyticity. Zbl 0978.53065Agrachev, Andrei A.; Sarychev, Andrei V. 10 1999 On the Dido problem and plane isoperimetric problems. Zbl 0977.53068Agrachev, Andrei A.; Gauthier, Jean-Paul A. 7 1999 A Hamiltonian approach to strong minima in optimal control. Zbl 0937.49012Agrachev, 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 0986.53009Agrachev, A. A.; Gauthier, J. P. A. 1 1999 Compactness for sub-Riemannian length–minimizers and subanalyticity. Zbl 1039.53038Agrachev, A. 18 1998 Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals. Zbl 0972.49014Agrachev, A. A. 16 1998 Sub-Riemannian metrics on \(\mathbb{R}^3\). Zbl 0962.53022Agrachev, A. A.; Chakir El-A., El-H.; Gauthier, J. P. 15 1998 Symplectic methods for optimization and control. Zbl 0965.93034Agrachev, A.; Gamkrelidze, R. 12 1998 An invariant second variation in optimal control. Zbl 0945.49015Agrachev, A.; Stefani, G.; Zezza, P. 8 1998 Strong minima in optimal control. Zbl 0936.49014Agrachev, A.; Stefani, G.; Zezza, P. 2 1998 Feedback-invariant optimal control theory and differential geometry. I: Regular extremals. Zbl 0952.49019Agrachev, A. A.; Gamkrelidze, R. V. 45 1997 Sub-Riemannian sphere in Martinet flat case. Zbl 0902.53033Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I. 34 1997 On Morse theory for piecewise smooth functions. Zbl 0951.49024Agrachev, A. A.; Pallaschke, D.; Scholtes, S. 8 1997 Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023Agrachev, A. A.; Sarychev, A. V. 39 1996 Exponential mappings for contact sub-Riemannian structures. Zbl 0941.53022Agrachev, A. A. 35 1996 Generic singularities of sub-Riemannian metrics on \(\mathbb{R}^ 3\). Zbl 0843.53025Agrachev, Andrei; El Alaoui, El-Houcine Chakir; Gauthier, Jean-Paul; Kupka, Ivan 3 1996 On abnormal extremals for Lagrange variational problems. Zbl 0826.49012Agrachev, A. A.; Sarychev, A. V. 19 1995 Strong minimality of abnormal geodesics for \(2\)-distributions. Zbl 0951.53029Agrachëv, A. A.; Sarychev, A. V. 16 1995 Methods of control theory in nonholonomic geometry. Zbl 0848.93012Agrachev, Andrej A. 9 1995 On regularity properties of extremal controls. Zbl 0951.49004Agrachëv, A. A. 5 1995 On the orbits of groups of diffeomorphisms and flows. Zbl 0902.58004Agrachev, A. A.; Gamkrelidze, R. V. 1 1995 The shuffle product and symmetric groups. Zbl 0790.05095Agrachev, A. A.; Gamkrelidze, R. V. 5 1994 Local controllability and semigroups of diffeomorphisms. Zbl 0787.93010Agrachev, A. A.; Gamkrelidze, R. V. 7 1993 Local controllability for families of diffeomorphisms. Zbl 0778.93003Agrachev, 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 0772.46021Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V. 3 1992 Symplectic geometry and necessary conditions for optimality. Zbl 0776.49014Agrachev, A. A.; Gamkrelidze, R. V. 1 1992 Symplectic geometry and necessary optimality conditions. Zbl 0729.49018Agrachev, A. A.; Gamkrelidze, R. V. 9 1991 Newton diagrams and tangent cones to attainable sets. Zbl 0811.93006Agrachev, A. A. 6 1991 Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0727.58009Agrachev, A. A.; Gamkrelidze, R. V. 6 1991 Morse theory and optimal control problems. Zbl 0743.58008Agrachev, 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 0762.46028Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V. 4 1991 ...and 27 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,096 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 Beauchard, Karine 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 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 996 more Authors all top 5 Cited in 256 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 27 Automatica 23 Proceedings of the Steklov Institute of Mathematics 22 Journal of Differential Equations 20 Annales de l’Institut Henri Poincaré. 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Académie des Sciences, Paris 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 Mathematical Control and Related Fields 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Sbornik: Mathematics 7 European Journal of Control 7 Journal of the European Mathematical Society (JEMS) 6 Communications in Mathematical Physics 6 Journal of the Franklin Institute 6 Journal of Mathematical Imaging and Vision 6 Journal of Nonlinear Science 6 Russian Journal of Nonlinear Dynamics 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. 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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 156 more Serials all top 5 Cited in 58 Fields 415 Differential geometry (53-XX) 394 Calculus of variations and optimal control; optimization (49-XX) 390 Systems theory; control (93-XX) 176 Global analysis, analysis on manifolds (58-XX) 140 Partial differential equations (35-XX) 112 Dynamical systems and ergodic theory (37-XX) 101 Ordinary differential equations (34-XX) 99 Mechanics of particles and systems (70-XX) 94 Topological groups, Lie groups (22-XX) 45 Fluid mechanics (76-XX) 44 Nonassociative rings and algebras (17-XX) 42 Numerical analysis (65-XX) 40 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) 22 Manifolds and cell complexes (57-XX) 20 Measure and integration (28-XX) 19 Real functions (26-XX) 19 Functional analysis (46-XX) 18 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) 8 Linear and multilinear algebra; matrix theory (15-XX) 8 Geometry (51-XX) 8 General topology (54-XX) 8 Statistical mechanics, structure of matter (82-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 General and overarching topics; collections (00-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 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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