Hamilton   Hamilton-Jacobi et théorie KAM faible
  À l'interface des EDP, systèmes dynamiques, lagrangiens et symboliques
ANR-07-BLAN-0361
   
Programme blanc KAMFAIBLE
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Bibliographie
Dernière mise à jour
29 septembre 2007



  • O. Alvarez, P. Cardaliaguet, R. Monneau. Existence and uniqueness for dislocation dynamics with nonnegative velocity. Interfaces Free Bound.7 (2005), no. 4, pp. 415--434.
  • N. Anantharaman. Entropy and the localization of eigenfunctions, Annals of Math. A paraître 2007.
  • N. Anantharaman, S. Zelditch. Patterson--Sullivan distributions and quantum ergodicity, Ann. I.H.P.
  • N. Anantharaman, R. Iturriaga, P. Padilla, H. Sanche. Physical solutions of the Hamilton-Jacobi equation, Disc. Cont. Dyn. Syst. B 5 no. 3, 513-528.
  • N. Anantharaman. On the zero-temperature or vanishing viscosity limit for Markov processes arising from Lagrangian dynamics, J. Eur. Math. Soc. 6 no. 2, 207-276.
  • A. Baraviera, A. Lopes, Ph. Thieullen. A large deviation principle for equilibrium states of Hölder potentials : the zero temperature case. Stochastics and Dynamics, Vol. 6 (2006), pp. 77-96.
  • N. Anantharaman. Counting geodesics which are optimal in homology, Ergodic Theory Dyn. Syst., 23 no. 2, 353-388.
  • M.-C. Arnaud. Approximation des ensembles omega-limites des difféomorphismes par des orbites périodiques Ann. Sci. Ecole Norm. Sup. (4) 36 (2003), 173-190.
  • M.-C. Arnaud, C. Bonatti et S. Crovisier. Dynamiques symplectiques génériques, Erg. Th. & Dyn. Sys. 25 (2005), 1401-1436.
  • M.-C. Arnaud. Convergence of the semi-group of Lax-Oleinik: a geometric point of view, Nonlinearity 18 (2005), 1835-1840.
  • M.-C. Arnaud. Type des orbites périodiques des flots associés à des langrangiens optiques homogènes Bull. Braz. Math. Soc. 37(2) (2006), 153-190.
  • M.-C. Arnaud. Hyperbolic periodic orbits and Mather sets in certain symmetric cases. Ergodic Theory Dynam. Systems 26 (2006), no. 4, 939-959
  • G. Barles, S. Biton. A Geometrical Approach to the Study of Unbounded Solutions of Quasilinear Parabolic Equations. Arch. Rational Mech. Anal. 162:4 (2002), 287-325.
  • G. Barles, J.M. Roquejoffre. Large time behaviour of fronts governed by eikonal equations. Interfaces Free Boundaries, 5, no. 1, 83--102.
  • G. Barles, F. Da Lio. On the Boundary Ergodic Problem for Fully Nonlinear Equations in Bounded Domains with General Nonlinear Neumann Boundary Conditions. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 5, 521--541.
  • G. Barles, O. Ley. Nonlocal first-order Hamilton-Jacobi equations modelling dislocations dynamics. Comm. Partial Differential Equations, 31 (2006), no. 7-9, 1191--1208.
  • G. Barles, J.M. Roquejoffre. Ergodic type problems and large time behavior of solutions of Hamilton-Jacobi Equations in an unbounded framework. Comm. Partial Differential Equations 31, no. 7-9, 1209--1225.
  • G. Barles. Some Homogenization Results for Non-Coercive Hamilton-Jacobi Equations. A paraître dans Calculus of Variations and Partial Differential Equations (2007).
  • P. Bernard. Hamiltonian systems: stability and unstability theory, Encyclopedia of Math Phys, Françoise, Naber, Tsun, éditeurs, Elsevier (2006)
  • P.Bernard, B. Buffoni. Optimal mass transportation and Mather theory, J. Eur. Math. Soc. 9 (2007), no. 1, 85-121.
  • P. Bernard. Symplectic aspects of Mather theory, Duke Math. J.136 (2007) no.3, 401-420.
  • P. Bernard, B. Buffoni.The Monge problem for supercritial Mané Potentials, Adv. in Math. 207 (2006), no. 2, 691-706.
  • P. Bernard. The asymptotic behaviour of solutions of the forced Burgers equation on the circle, Nonlinearity, 18 (2005), 101-124.
  • T. Bousch. La condition de Walters, Ann. Sci. ENS 34 (2001), 287-311.
  • T. Bousch, J.Mairesse. Asymptotic height optimization for topical IFS, Tetris heaps,and the finiteness conjecture, Journal of AMS, 15 (2002), 77-111.
  • T. Bousch. Un lemme de Mané bilatéral, CRAS Paris Ser. I, 335 (2002), 533-536.
  • T. Bousch, O.Jenkinson. Cohomology classes of dynamically non-negative Ck functions, Invent. Math. 148 (2002), 207-217.
  • T. Bousch. Nouvelle preuve d'un théorème de Yuan et Hunt, manuscrit (2006).
  • L. Caffarelli, J.-M. Roquejoffre. Uniform Holder estimates in singularly perturbed elliptic systems and applications to models for diffusion flames. A paraître dans Archive for Rational Mechanics and Analysis (2007).
  • P. Cannarsa, P. Cardaliaguet. Perimeter estimates for reachable sets of control systems. J. Convex Anal. 13 (2006), no. 2, 253-267.
  • P. Cardaliaguet, O. Ley. On some flows in shape optimization. Arch. Ration. Mech.Anal. 183 (2007), no. 1, 21-58.
  • A. Chenciner, A. Venturelli. Minima de l'intégrale d'action du Problème newtonien de 4 corps de masses égales : orbites Hip-Hop, Celestial Mechanics 77, p. 139-152, (2000).
  • A. Chenciner. Action minimizing periodic orbits in the Newtonian n-body problem, Contemp. Math. 292 (2002), AMS, p.71-90.
  • A. Chenciner. Action minimizing solutions of the n-body problem: from homology to symmetry, Proceedings du Congrés international des mathŕmaticiens (ICM), Pékin, aout 2002, vol. III, p. 279-294.
  • A. Chenciner. Perverse solutions of the planar n-body problem, S.M.F. Astérisque 287 (2003), pages 249-256.
  • A. Chenciner, J. Féjoz, R. Montgomery, Rotating Eights I : the three Gammai families, Nonlinearity 18 (2005) 1407-1424.
  • A. Chencincer, J. Féjoz , L' équation aux variations verticales d'un équilibre relatif comme source de nouvelles solutions périodiques du problème des N corps, C.R. Acad. Sci. Paris, Ser. I 340 (2005), 593-598.
  • A. Chenciner, J. Féjoz. The flow of the equal-mass spatial three-body problem in the neighborhood of the equilateral relative equilibrium, soumis (juin 2006).
  • Y. Chitour, F. Jean, E. Trélat. Genericity results for singular curves, J. Differential Geom. 73, 1 (2006),  45–73.
  • G. Contreras , A. Lopes, Ph. Thieullen. Lyapunov minimizing measures for expanding maps of the interval, Erg. Th. Dyn. Sys., Vol. 21 (2001), pp. 1379-1409.
  • D. Cordero-Erausquin, B. Nazaret, C. Villani. A new approach to sharp Sobolev and Gagliardo--Nirenberg inequalities, Adv. Math. 182, 2 (2004), 307--332.
  • J.-M. Coron, E. Trélat. Global steady-state controllability of 1-D semilinear heat equations, SIAM J. Control Optim. 43, 2 (2004), 549–569.
  • L. Desvillettes, C. Villani. On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation. Invent. Math. 159, 2 (2005), 245--316.
  • J. Droniou, C. Imbert. Fractal first order partial differential equations, Archive for Rational Mechanics and Analysis, Vol 182, (2006), pp. 299-331
  • J. Droniou, C. Imbert, J. Vovelle. An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions, Annales de l'Institut Henri Poincaré - Analyse non linéaire, Vol 21, (2004), pp. 689-714
  • A. Fathi, A. Siconolfi. Existence of C1 critical subsolutions of the Hamilton-Jacobi equation, Invent. Math, 155 (2004), pp. 363-388.
  • A. Fathi, A. Siconolfi. PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians, Calc. Var. Partial Differential Equations, 22 (2005) pp. 185-228.
  • A. Fathi. Weak KAM Theorem in Lagrangian Dynamics, livre à paraître, Cambridge University Press
  • A. Fathi. Sard, Whitney, Assouad and Mather, Oberwolfach Reports, 2 (2005) p.p. 1766-17667.
  • A. Fathi, E. Maderna. Weak KAM theorem on non compact manifolds, à paraître NoDEA
  • J. Féjoz. Démonstration du "théorème d'Arnold" sur la stabilité du système planétaire (d'après M. Herman), Ergodic Theory and Dynamical Systems 24:5 (2004) 1521-1582.
  • J. Féjoz. Global secular dynamics in the planar three-body problem, Celest. Mech. and Dynam. Astronom. 84 (2002), 159-195.
  • A. Figalli, C. Villani. Strong displacement convexity on Riemannian manifolds, à paraître Math. Z.
  • E. Garibaldi et A. Lopes, Ph. Thieullen. On separating sub-actions, 15 pages, soumis.
  • F. Hamel, R. Monneau, J.-M. Roquejoffre. Stability of travelling waves in a model for conical flames in two space dimensions. Ann. Sci. École Norm. Sup. 4:3, 469--506.
  • F. Hamel, R. Monneau, J.-M. Roquejoffre. Asymptotic properties and classification of bistable fronts with Lipschitz level sets. Discrete Contin. Dyn. Syst. 14 no. 1, 75--92.
  • C. Imbert, R. Monneau. Homogenization of first order equations with u/epsilon-periodic Hamiltonians. Part I: local equations, à paraître Communications in Partial Differential Equations.
  • C. Imbert. Convexity of solutions and C1,1 estimates for fully nonlinear elliptic equations,, Journal de Mathématiques Pures et Appliquées, Vol 85, (2006), pp. 791-807
  • C. Imbert, J. Vovelle, A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications, SIAM - Mathematical Analysis, Vol 36, Issue 1 (2004), pp. 214-232
  • O. Ley. Lower-bound gradient estimates for first-order Hamilton-Jacobi equations and applications to the regularity of propagating fronts. Adv. Differential Equations, 6:5 (2001), 547-576.
  • F. Da Lio, O. Ley. Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications.SIAM J. Control Optim., 45: (2006) : 74-106.
  • A. Lopes, Ph. Thieullen. Sub-actions for Anosov diffeomorphisms, Proc. Geometric Methods in Dynamics, Ed. W. de Melo, M. Viana, Astérisque et J.C. Yoccoz, 287 (2003), pp. 115-146.
  • A. Lopes, Ph. Thieullen. Sub-actions for flows, Ergodic Theory and Dynamical System, Vol. 25 (2005), pp. 605-628
  • A. Lopes, Ph. Thieullen. Mather measures and the Bowen-Series transformations, Ann. Inst. Henri Poincaré, Analyse non linéaire, 23 (2006), 663—682.
  • A. Lopes, Ph. Thieullen. Eigenfunctions of the Laplacian and eigenfunctions of the associated Ruelle operator, 21 pages, soumis.
  • J. Lott, C. Villani. Ricci curvature for metric-measure spaces via optimal transport, à paraître Ann. of Math.
  • E. Maderna, A. Venturelli. Globally minimizing parabolic motions in the Newtonian N-body Problem, (2007).
  • D. Massart. Normes stables des surfaces, C.R A.S. t. 324, Série I, (1997) p. 221-224.
  • D. Massart. Stable norms of surfaces: local structure of the unit ball of rational directions Geom. Funct. Anal. 7, 6, (1997) 996-1010.
  • D. Massart. On Aubry sets and Mather's action functional Israel Journal of Mathematics 134, (2003) 157-171.
  • D. Massart. Subsolutions of time-periodic Hamilton-Jacobi equations, à paraître à Ergodic Theory and Dynamical systems 2007
  • D. Massart. Vertices of Mather's beta function, II preprint 2007
  • L. Rifford, E. Trélat. Morse-Sard type results in sub-Riemannian geometry, Math. Ann. 332, 1 (2005), 145–159.
  • L. Rifford. A propos des sphères sous-riemanniennes, Bull. Belg. Math. Soc. Simon Stevin 13 (2006), 521-526.
  • L. Rifford. On the existence of local smooth repulsive stabilizing feedbacks in dimension three, J. Differential Equations 226 (2006), 429-500.
  • L. Rifford. Stratified semiconcave control-Lyapunov functions and the stabilization problem, Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005), no. 3, 343-384.
  • L. Rifford. A Morse-Sard theorem for the distance function on Riemannian manifolds, Manuscripta Math. 113 (2004), 251-265.
  • S. Terracini, A. Venturelli. Symmetric trajectories for the 2N-body problem with equal masses, à paraître dans Archive for Rational Mechanics and Analysis (2007).
  • E. Trélat. Global subanalytic solutions of Hamilton-Jacobi type equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 23, 3 (2006), 363–387. 
  • E. Trélat. Contrôle optimal : théorie et applications, Vuibert, Collection "Mathématiques Concrètes" (2005), 246 pages. ISBN 2 7117 7175 X.
  • A. Venturelli. Une caractérisation variationnelle des solutions de Lagrange du Problème plan des trois corps, C.R. Acad. Sci. Paris, t. 332, Sèrie I, pp. 641-644, (2001).
  • A. Venturelli. A Variational proof of the existence of Von Schubart orbit, soumis à Discrete and Continuous Dynamical Systems, (2006).
  • C. Villani. Topics in Optimal Transportation, Graduate Studies in Mathematics 58, American Mathematical Society, Providence (2003).
contact
Philippe Thieullen