Andrei A. Agrachev
Submitted
[133] A.A. Agrachev, D. Barilari, U. Boscain, Introduction to geodesics in sub-Riemannian geometry2015
[132] A.A. Agrachev, Tangent hyperplanes to subriemannian balls[131] A.A. Agrachev, D. Barilari, L. Rizzi, Curvature: a variational approach
[130] A.A. Agrachev, D. Barilari, L. Rizzi, Sub-Riemannian curvature in contact geometry
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[129] A.A. Agrachev, A. Gentile, A. Lerario, Geodesics and horizontal-path spaces in Carnot groups
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[128] A.A. Agrachev, L. Rizzi, P. Silveira, On conjugate times of LQ optimal control problems
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[127] A.A. Agrachev, Quadratic cohomology
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[126] A.A. Agrachev, P. Lee, Bishop and Laplacian comparison theorems on 3D contact sub-Riemannian manifolds with symmetry
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2014
[125] A.A. Agrachev, Some open problems[124] A.A. Agrachev, P. Lee, Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds
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2013
[123] A. A. Agrachëv, D. V. Anosov, S. M. Aseev, V. M. Buchstaber, A. M. Vershik, Ya. B. Vorobets, V. A. Kaimanovich, B. S. Kashin, I. G. Lysënok, A. Yu. Ol'shanskii, V. N. Remeslennikov, Ya. G. Sinai, S. K. Smirnov, A. M. Stepin, I. A. Taimanov, E. V. Shchepin, Rostislav Ivanovich Grigorchuk (on his sixtieth birthday)2012
[122] A.A. Agrachev, D. Barilari, U. Boscain, Introduction to Riemannian and sub-Riemannian geometry![](/wp-content/uploads/2014/08/arrow_down_eng.png)
[121] A. A. Agrachev, D. V. Anosov, I. A. Bogaevskii, A. S. Bortakovskii, A. B. Budak, V. A. Vassiliev, V. V. Goryunov, S. M. Gusein-Zade, A. A. Davydov, V. R. Zarodov, V. D. Sedykh, D. V. Treshchev, V. N. Chubarikov, Vladimir Mikhailovich Zakalyukin (obituary)
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[120] A.A. Agrachev, A. Lerario, Systems of quadratic inequalities
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[119] A.A. Agrachev, Yu. Baryshnikov, D. Liberzon, On robust Lie-algebraic stability conditions for switched linear systems
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[118] A.A. Agrachev, D. Barilari, Sub-Riemanian structures on 3D Lie groups
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[117] A.A. Agrachev, D. Barilari, U. Boscain, On the Hausdorff volume in sub-Riemannian geometry
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2011
[116] A.A. Agrachev, R.V. Gamkrelidze, The geometry of maximum principle[115] A.A. Agrachev, On the space of symmetric operators with multiple ground states
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2010
[114] Yu. S. Osipov, V. V. Kozlov, L. D. Faddeev, D. V. Anosov, V. S. Vladimirov, R. V. Gamkrelidze, A. A. Gonchar, N. N. Krasovskii, A. V. Kryazhimskii, A. B. Kurzhanskii, S. P. Novikov, S. M. Aseev, A. B. Zhizhchenko, D. V. Treschev, A. A. Agrachev, E. A. Volkov, N. L. Grigorenko, A. A. Davydov, M. I. Zelikin, A. Yu. Kolesov, A. A. Mal'tsev, M. S. Nikol'skii, N. Kh. Rozov, A. G. Sergeev, K. O. Besov, S. P. Konovalov, In memory of Evgenii Frolovich Mishchenko[113] A.A. Agrachev, Invariant Lagrange submanifolds of dissipative systems
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[112] A.A. Agrachev, P. Lee, Continuity of optimal control costs and its application to weak KAM theory
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[111] A.A. Agrachev, U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti, Two-dimensional almost-Riemannian structures with tangency points
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[110] A.A. Agrachev, Well-posed infinite horizon variational problems on a compact manifold
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[109] A.A. Agrachev, M. Caponigro, Dynamics control by a time-varying feedback
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2009
[108] A.A. Agrachev, Any sub-Riemannian metric has points of smoothness![](/wp-content/uploads/2014/08/arrow_down_eng.png)
[107] A.A. Agrachev, U. Boscain, J.-P. Gauthier, F. Rossi, The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
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[106] A.A. Agrachev, M. Caponigro, Controllability on the group of diffeomorphisms
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[105] A.A. Agrachev, P. Lee, Optimal transportation under nonholonomic constraints
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[104] A.A. Agrachev, F. Chittaro, Smooth optimal synthesis for infinite horizon variational problems
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2008
[103] A.A. Agrachev, F.C. Chittaro, Extremals flows and infinite horizon optimization[102] A.A. Agrachev, Hamiltonian systems and optimal control
[101] A.A. Agrachev, Geometry of optimal control problems and Hamiltonian systems
[100] A.A. Agrachev, M. Caponigro, Families of vector fields which generate the group of diffeomorphisms
[99] A.A. Agrachev, U. Boscain, M. Sigalotti, A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds
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2007
[98] A.A. Agrachev, The Curvature and Hyperbolicity of Hamiltonian Systems![](/wp-content/uploads/2014/08/arrow_down.png)
[97] A.A. Agrachev, Optimal control of measures
[96] A.A. Agrachev, A.V. Sarychev, Solid controllability in fluid dynamics
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[95] A.A. Agrachev, Rolling balls and Octonions
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[94] A.A. Agrachev, S. Kuksin, A. Sarychev, A. Shirikyan, On finite-dimensional projections of distributions for solutions of randomly forced PDE's
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[93] A.A. Agrachev, I. Zelenko, On feedback classification of generic control-affine systems with one- and two-dimensional inputs
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2006
[92] A.A. Agrachev, R.V. Gamkrelidze, Vector fields on![n](http://control.botik.ru/wp-content/plugins/latex/cache/tex_7b8b965ad4bca0e41ab51de7b31363a1.gif)
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[91] A.A. Agrachev, I. Zelenko, Nurowski's conformal structures for (2,5)-distributions via dynamics of abnormal extremals
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[90] A.A. Agrachev, R.V. Gamkrelidze, The Pontryagin Maximum Principle 50 years later
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[89] A.A. Agrachev, A.V. Sarychev, Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing
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[88] A.A. Agrachev, T. Chambrion, An estimation of the controllability time for single-input systems on compact Lie groups
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2005
[87] A.A. Agrachëv, N.N. Shcherbakova, Hyperbolicity of Hamiltonian systems of negative curvature[86] A.A. Agrachev, N. Chtcherbakova, I. Zelenko, On curvatures and focal points of dynamical Lagrangian distributions and their reductions by first integrals
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[85] A.A. Agrachev, N.N. Chtcherbakova, Hamiltonian systems of negative curvature are hyperbolic
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[84] A.A. Agrachev, A. Marigo, Rigid Carnot algebras: classification
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[83] A.A. Agrachev, A.V. Sarychev, Navier-Stokes equations: controllability by means of low modes forcing
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[82] A.A. Agrachev, Yu.L. Sachkov, Control theory from the geometric viewpoint
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2004
[81] A.A. Agrachëv, A.V. Sarychev, Controllability for the Navier-Stokes equation with small control[80] A.A. Agrachev, Yu. L. Sachkov, Control theory from the geometric viewpoint
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2003
[79] A.A. Agrachev, A. Marigo, Nonholonomic tangent spaces: intrinsic construction and rigid dimensions![](/wp-content/uploads/2014/08/arrow_down_eng.png)
[78] A.A. Agrachev, M. Sigalotti, On the local structure of optimal trajectories in
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2002
[77] A. A. Agrachev, Introduction to optimal control theory[76] A.A. Agrachev, I. Zelenko, Geometry of Jacobi curves, II
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[75] A.A. Agrachev, I. Zelenko, Geometry of Jacobi curves, I
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[74] A.A. Agrachev, G. Stefani, P. Zezza, Strong optimality for a bang-bang trajectory
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2001
[73] A. A. Agrachev, D. Liberzon, Lie-algebraic stability criteria for switched systems[72] A.A. Agrachev, J.-P. Gauthier, On the subanalyticity of Carnot-Caratheodory distances
[71] A.A. Agrachev, I. Zelenko, Principal invariants of Jacobi curves
[70] A.A. Agrachev, J.-P. Gauthier, Subanalyticity of distance and spheres in sub-Riemannian geometry
[69] A.A. Agrachev, A "Gauss-Bonnet formula" for contact sub-Riemannian manifolds
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[68] A.A. Agrachev, J.-P. Gauthier, On subanalyticity of Carnot-Caratheodory distances
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[67] A.A. Agrachev, D. Liberzon, Lie-Algebraic conditions for exponential stability of switched systems
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[66] A.A. Agrachev, Yu. L. Sachkov, Optimal control problem for a nonlinear driftless 5-dimensional system with 2 inputs
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2000
[65] A. A. Agrachev, G. Stefani, P. Zezza, Symplectic methods for strong local optimality in the bang-bang case[64] A.A. Agrachev, G. Charlot, J.-P. A. Gauthier, V. M. Zakalyukin, On stability of generic subriemannian caustic in the three-space
[63] A.A. Agrachev, J.-P. Gauthier, V. Zakalyukin, On sub-Riemannian caustics and wave fronts for contact distributions in the three-space
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1999
[62] A.A. Agrachev, G. Stefani, P. Zezza, A Hamiltonian approach to strong minima in optimal control[61] A. A. Agrachev, J.-P. A. Gauthier, Sub-Riemannian metrics and isoperimetric problems in the contact case
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[60] A.A. Agrachev, J.-P. Gauthier Sub-Riemannian metrics and isoperimetric problems in the contact case
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[59] A.A. Agrachev, A.V. Sarychev, Sub-Riemannian metrics: minimality of abnormal geodesics versus subanalyticity
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[58] A.A. Agrachev, J.-P. Gauthier, On the Dido problem and plane isoperimetric problems
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[57] A.A. Agrachev, Is it possible to recognize Local Controllability in a finite number of differentiations?
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[56] A.A. Agrachev, Yu. L. Sachkov, An Intrinsic Approach to the Control of Rolling Bodies
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1998
[55] A.A. Agrachev, G. Stefani, P. Zezza, An invariant second variation in optimal control[54] A. A. Agrachev, P. Zezza, G. Stefani, Strong minima in optimal control
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[53] A. A. Agrachev, E. F. Mishchenko, Introduction. On works of R. V. Gamkrelidze
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[52] A.A. Agrachev, Compactness for sub-Riemannian length-minimizers and subanalyticity
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[51] A.A. Agrachev, On the equivalence of different types of local minima in sub-Riemannian problems
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[50] A.A. Agrachev, Feedback-invariant optimal control theory and differential geometry, II. Jacobi curves for singular extremals
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[49] A.A. Agrachev, H. Chakir, J.-P. Gauthier, Sub-Riemannian metrics on
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[48] A.A. Agrachev, R.V. Gamkrelidze, Symplectic methods for optimization and control
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1997
[47] A.A. Agrachev, S. Scholtes, D. Pallaschke, On Morse theory for piecewise smooth functions![](/wp-content/uploads/2014/08/arrow_down_eng.png)
[46] A.A. Agrachev, R.V. Gamkrelidze, Feedback-invariant optimal control theory and differential geometry, I. Regular extremals
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[45] A.A. Agrachev, B. Bonnard, M. Chyba, I. Kupka, Sub-Riemannian sphere in Martinet flat case
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1996
[44] A.A. Agrachev, El Alaoui El-Houcine Chakir, Gauthier Jean-Paul, I. Kupka, Generic singularities of sub-Riemannian metrics on![R3](http://control.botik.ru/wp-content/plugins/latex/cache/tex_5c108ce0fe89d0632cfce75f650b36c2.gif)
[43] A.A. Agrachev, Exponential mappings for contact sub-Riemannian structures
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[42] A.A. Agrachev, A.V. Sarychev, Abnormal sub-Riemannian geodesics: Morse index and rigidity
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1995
[41] A. A. Agrachev, R. V. Gamkrelidze, On the orbits of groups of diffeomorphisms and flows![](/wp-content/uploads/2014/08/arrow_down.png)
[40] A.A. Agrachev, On regularity properties of extremal controls
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[39] A.A. Agrachev, Methods of control theory in nonholonomic geometry
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[38] A.A. Agrachev, A.V. Sarychev, Strong minimality of abnormal geodesics for 2-distributions
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[37] A.A. Agrachev, A.V. Sarychev, On abnormal extremals for Lagrange variational problems
1994
[36] A.A. Agrachev, R.V. Gamkrelidze, The shuffle product and symmetric groups1993
[35] A.A. Agrachev, R.V. Gamkrelidze, Local Controllability and Semigroups of Diffeomorphisms![](/wp-content/uploads/2014/08/arrow_down_eng.png)
[34] A.A. Agrachev, R.V. Gamkrelidze, Local controllability for families of diffeomorphisms
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1991
[33] E. R. Avakov, A. A. Agrachev, A. V. Arutyunov, The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping![](/wp-content/uploads/2014/08/arrow_down.png)
[32] A.A. Agrachev, R.V. Gamkrelidze, Volterra series and groups of permutations
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[31] A.A. Agrachev, R.V. Gamkrelidze, Symplectic geometry and necessary conditions for optimality
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1990
[30] A.A. Agrachëv, R.V. Gamkrelidze, The “time substitution” variation in optimal control[29] A.A. Agrachev, Newton diagrams and tangent cones to attainable sets
[28] A.A. Agrachev, R.V. Gamkrelidze, Symplectic geometry for optimal control
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[27] A.A. Agrachev, Quadratic mappings in geometric control theory
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1989
[26] A. A. Agrachev, One more condition for a conditional extremum![](/wp-content/uploads/2014/08/arrow_down.png)
[25] A.A. Agrachev, S.A. Vakhrameev, Morse theory and optimal control problems
[24] A.A. Agrachev, One more condition for a conditional extremum
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[23] A.A. Agrachev, R.V. Gamkrelidze, Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets
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[22] A.A. Agrachev, R.V. Gamkrelidze, The quasi-extremality for controlled systems
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[21] A.A. Agrachev, R.V. Gamkrelidze, S.A. Vakhrameev, Ordinary differential equations on vector bundles and the chronological calculus
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[20] A.A. Agrachev, A.V. Sarychev, R.V. Gamkrelidze, Local invariants of smooth control systems
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1988
[19] A. A. Agrachev, Quadratic mappings in geometric control theory![](/wp-content/uploads/2014/08/arrow_down.png)
[18] A.A. Agrachëv, A.V. Sarychev, Filtrations of a Lie algebra of vector fields and the nilpotent approximation of controllable systems
[17] A.A. Agrachev, Topology of quadratic mappings and Hessians of smooth mappings
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[16] A.A. Agrachev, Homology of the intersections of real quadrics
[15] A.A. Agrachev, R.V. Gamkrelidze, Computation of the Euler characteristic of intersections of real quadrics
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1987
[14] A.A. Agrachev, A.V. Sarychev, Filtrations of a Lie algebra of vector fields and nilpotent approximation of controlled systems![](/wp-content/uploads/2014/08/arrow_down_eng.png)
1986
[13] A. A. Agrachev, S. A. Vakhrameev, Linearly controlled systems of constant rank and relay conditions for extreme control![](/wp-content/uploads/2014/08/arrow_down.png)
[12] A.A. Agrachev, A.V. Sarychev, On reduction of a smooth system linear in the control
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[11] A.A. Agrachev, R.V. Gamkrelidze, The Morse index and the Maslov index for smooth control systems
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1985
[10] A.A. Agrachev, R.V. Gamkrelidze, The index of extremality and quasiextremal controls![](/wp-content/uploads/2014/08/arrow_down_eng.png)
1984
[9] A.A. Agrachev, S.A. Vakhrameev, Nonlinear control systems of constant rank and bang-bang conditions for extremal controls1983
[8] A.A. Agrachëv, A.V.Sarychev, The control of rotation for an asymmetric rigid body[7] A. A. Agrachev, S. A. Vakhrameev, R. V. Gamkrelidze, Differential geometric and group theoretic methods in optimal control theory
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1981
[6] A.A. Agrachev, S.A. Vakhrameev, Chronological series and Cauchy - Kovalevska theorem![](/wp-content/uploads/2014/08/arrow_down_eng.png)
1980
[5] A.A. Agrachev, Gamkrelidze R.V., The chronological algebras and nonstationary vector fields![](/wp-content/uploads/2014/08/arrow_down_eng.png)
1978
[4] A.A. Agrachev, Gamkrelidze R.V., The exponential representation of flows and the chronological calculus![](/wp-content/uploads/2014/08/arrow_down_eng.png)
1977
[3] A.A. Agrachev, A second-order necessary condition for optimality in the general nonlinear case![](/wp-content/uploads/2014/08/arrow_down_eng.png)
1976
[2] A.A. Agrachev, R.V. Gamkrelidze, A second order optimality principle for a time-optimal problem![](/wp-content/uploads/2014/08/arrow_down_eng.png)
1974
[1] A.A. Agrachev, On superpositions of continuous functions![](/wp-content/uploads/2014/08/arrow_down_eng.png)