Andrei A. Agrachev

Submitted

[133] A.A. Agrachev, D. Barilari, U. Boscain, Introduction to geodesics in sub-Riemannian geometry

2015

[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  
[129] A.A. Agrachev, A. Gentile, A. Lerario, Geodesics and horizontal-path spaces in Carnot groups  
[128] A.A. Agrachev, L. Rizzi, P. Silveira, On conjugate times of LQ optimal control problems  
[127] A.A. Agrachev, Quadratic cohomology  
[126] A.A. Agrachev, P. Lee, Bishop and Laplacian comparison theorems on 3D contact sub-Riemannian manifolds with symmetry  

2014

[125] A.A. Agrachev, Some open problems
[124] A.A. Agrachev, P. Lee, Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds  

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  
[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)   
[120] A.A. Agrachev, A. Lerario, Systems of quadratic inequalities  
[119] A.A. Agrachev, Yu. Baryshnikov, D. Liberzon, On robust Lie-algebraic stability conditions for switched linear systems  
[118] A.A. Agrachev, D. Barilari, Sub-Riemanian structures on 3D Lie groups  
[117] A.A. Agrachev, D. Barilari, U. Boscain, On the Hausdorff volume in sub-Riemannian geometry  

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   

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   
[112] A.A. Agrachev, P. Lee, Continuity of optimal control costs and its application to weak KAM theory  
[111] A.A. Agrachev, U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti, Two-dimensional almost-Riemannian structures with tangency points  
[110] A.A. Agrachev, Well-posed infinite horizon variational problems on a compact manifold  
[109] A.A. Agrachev, M. Caponigro, Dynamics control by a time-varying feedback  

2009

[108] A.A. Agrachev, Any sub-Riemannian metric has points of smoothness  
[107] A.A. Agrachev, U. Boscain, J.-P. Gauthier, F. Rossi, The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups  
[106] A.A. Agrachev, M. Caponigro, Controllability on the group of diffeomorphisms  
[105] A.A. Agrachev, P. Lee, Optimal transportation under nonholonomic constraints  
[104] A.A. Agrachev, F. Chittaro, Smooth optimal synthesis for infinite horizon variational problems  

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  

2007

[98] A.A. Agrachev, The Curvature and Hyperbolicity of Hamiltonian Systems  
[97] A.A. Agrachev, Optimal control of measures
[96] A.A. Agrachev, A.V. Sarychev, Solid controllability in fluid dynamics  
[95] A.A. Agrachev, Rolling balls and Octonions   
[94] A.A. Agrachev, S. Kuksin, A. Sarychev, A. Shirikyan, On finite-dimensional projections of distributions for solutions of randomly forced PDE's  
[93] A.A. Agrachev, I. Zelenko, On feedback classification of generic control-affine systems with one- and two-dimensional inputs  

2006

[92] A.A. Agrachev, R.V. Gamkrelidze, Vector fields on $n$-bundles over $2n$-dimensional manifolds
[91] A.A. Agrachev, I. Zelenko, Nurowski's conformal structures for (2,5)-distributions via dynamics of abnormal extremals  
[90] A.A. Agrachev, R.V. Gamkrelidze, The Pontryagin Maximum Principle 50 years later   
[89] A.A. Agrachev, A.V. Sarychev, Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing  
[88] A.A. Agrachev, T. Chambrion, An estimation of the controllability time for single-input systems on compact Lie groups  

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  
[85] A.A. Agrachev, N.N. Chtcherbakova, Hamiltonian systems of negative curvature are hyperbolic  
[84] A.A. Agrachev, A. Marigo, Rigid Carnot algebras: classification  
[83] A.A. Agrachev, A.V. Sarychev, Navier-Stokes equations: controllability by means of low modes forcing  
[82] A.A. Agrachev, Yu.L. Sachkov, Control theory from the geometric viewpoint   

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  

2003

[79] A.A. Agrachev, A. Marigo, Nonholonomic tangent spaces: intrinsic construction and rigid dimensions  
[78] A.A. Agrachev, M. Sigalotti, On the local structure of optimal trajectories in $R^3$  

2002

[77] A. A. Agrachev, Introduction to optimal control theory
[76] A.A. Agrachev, I. Zelenko, Geometry of Jacobi curves, II  
[75] A.A. Agrachev, I. Zelenko, Geometry of Jacobi curves, I  
[74] A.A. Agrachev, G. Stefani, P. Zezza, Strong optimality for a bang-bang trajectory  

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  
[68] A.A. Agrachev, J.-P. Gauthier, On subanalyticity of Carnot-Caratheodory distances  
[67] A.A. Agrachev, D. Liberzon, Lie-Algebraic conditions for exponential stability of switched systems  
[66] A.A. Agrachev, Yu. L. Sachkov, Optimal control problem for a nonlinear driftless 5-dimensional system with 2 inputs  

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  

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  
[60] A.A. Agrachev, J.-P. Gauthier Sub-Riemannian metrics and isoperimetric problems in the contact case  
[59] A.A. Agrachev, A.V. Sarychev, Sub-Riemannian metrics: minimality of abnormal geodesics versus subanalyticity  
[58] A.A. Agrachev, J.-P. Gauthier, On the Dido problem and plane isoperimetric problems  
[57] A.A. Agrachev, Is it possible to recognize Local Controllability in a finite number of differentiations?  
[56] A.A. Agrachev, Yu. L. Sachkov, An Intrinsic Approach to the Control of Rolling Bodies  

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  
[53] A. A. Agrachev, E. F. Mishchenko, Introduction. On works of R. V. Gamkrelidze  
[52] A.A. Agrachev, Compactness for sub-Riemannian length-minimizers and subanalyticity  
[51] A.A. Agrachev, On the equivalence of different types of local minima in sub-Riemannian problems  
[50] A.A. Agrachev, Feedback-invariant optimal control theory and differential geometry, II. Jacobi curves for singular extremals  
[49] A.A. Agrachev, H. Chakir, J.-P. Gauthier, Sub-Riemannian metrics on $R^3$  
[48] A.A. Agrachev, R.V. Gamkrelidze, Symplectic methods for optimization and control  

1997

[47] A.A. Agrachev, S. Scholtes, D. Pallaschke, On Morse theory for piecewise smooth functions  
[46] A.A. Agrachev, R.V. Gamkrelidze, Feedback-invariant optimal control theory and differential geometry, I. Regular extremals  
[45] A.A. Agrachev, B. Bonnard, M. Chyba, I. Kupka, Sub-Riemannian sphere in Martinet flat case  

1996

[44] A.A. Agrachev, El Alaoui El-Houcine Chakir, Gauthier Jean-Paul, I. Kupka, Generic singularities of sub-Riemannian metrics on $R3$
[43] A.A. Agrachev, Exponential mappings for contact sub-Riemannian structures  
[42] A.A. Agrachev, A.V. Sarychev, Abnormal sub-Riemannian geodesics: Morse index and rigidity  

1995

[41] A. A. Agrachev, R. V. Gamkrelidze, On the orbits of groups of diffeomorphisms and flows  
[40] A.A. Agrachev, On regularity properties of extremal controls  
[39] A.A. Agrachev, Methods of control theory in nonholonomic geometry  
[38] A.A. Agrachev, A.V. Sarychev, Strong minimality of abnormal geodesics for 2-distributions  
[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 groups

1993

[35] A.A. Agrachev, R.V. Gamkrelidze, Local Controllability and Semigroups of Diffeomorphisms  
[34] A.A. Agrachev, R.V. Gamkrelidze, Local controllability for families of diffeomorphisms  

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  
[32] A.A. Agrachev, R.V. Gamkrelidze, Volterra series and groups of permutations   
[31] A.A. Agrachev, R.V. Gamkrelidze, Symplectic geometry and necessary conditions for optimality  

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  
[27] A.A. Agrachev, Quadratic mappings in geometric control theory  

1989

[26] A. A. Agrachev, One more condition for a conditional extremum  
[25] A.A. Agrachev, S.A. Vakhrameev, Morse theory and optimal control problems
[24] A.A. Agrachev, One more condition for a conditional extremum  
[23] A.A. Agrachev, R.V. Gamkrelidze, Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets   
[22] A.A. Agrachev, R.V. Gamkrelidze, The quasi-extremality for controlled systems   
[21] A.A. Agrachev, R.V. Gamkrelidze, S.A. Vakhrameev, Ordinary differential equations on vector bundles and the chronological calculus  
[20] A.A. Agrachev, A.V. Sarychev, R.V. Gamkrelidze, Local invariants of smooth control systems  

1988

[19] A. A. Agrachev, Quadratic mappings in geometric control theory  
[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  
[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  

1987

[14] A.A. Agrachev, A.V. Sarychev, Filtrations of a Lie algebra of vector fields and nilpotent approximation of controlled systems  

1986

[13] A. A. Agrachev, S. A. Vakhrameev, Linearly controlled systems of constant rank and relay conditions for extreme control  
[12] A.A. Agrachev, A.V. Sarychev, On reduction of a smooth system linear in the control   
[11] A.A. Agrachev, R.V. Gamkrelidze, The Morse index and the Maslov index for smooth control systems  

1985

[10] A.A. Agrachev, R.V. Gamkrelidze, The index of extremality and quasiextremal controls  

1984

[9] A.A. Agrachev, S.A. Vakhrameev, Nonlinear control systems of constant rank and bang-bang conditions for extremal controls

1983

[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  

1981

[6] A.A. Agrachev, S.A. Vakhrameev, Chronological series and Cauchy - Kovalevska theorem  

1980

[5] A.A. Agrachev, Gamkrelidze R.V., The chronological algebras and nonstationary vector fields  

1978

[4] A.A. Agrachev, Gamkrelidze R.V., The exponential representation of flows and the chronological calculus  

1977

[3] A.A. Agrachev, A second-order necessary condition for optimality in the general nonlinear case  

1976

[2] A.A. Agrachev, R.V. Gamkrelidze, A second order optimality principle for a time-optimal problem  

1974

[1] A.A. Agrachev, On superpositions of continuous functions