Dynamical Systems

ISBN-13: 9780521860680 / Angielski / Twarda / 2006 / 596 str.

A. Fathi; J. -C Yoccoz

Opis

Michael Robert Herman had a profound impact on the theory of dynamical systems over the last 30 years. His seminar at the Ecole Polytechnique had major worldwide influence and was the main vector in the development of the theory of dynamical systems in France. His interests covered most aspects of the subject though closest to his heart were the so-called small divisors problems, in particular those related to the stability of quasiperiodic motions. This volume aims to reflect the depth and variety of these interests and the frontier of present research; a frontier shaped decisively by Michael Herman's contributions.

Recenzje

'Michael Robert Herman had a profound impact on the theory of dynamical systems over the last 30 years. This volume aims to reflect the depth and variety of these interests and the frontier of present research.' L'enseignement mathematique

Spis treści

1. Michael Robert Herman, 1942–2000 A. Fathi and J. C. Yoccoz; 2. L2 regularity of measurable solutions of a finite-difference equation of the circle Michael Robert Herman; 3. On Herman's theorem for ergodic, amenable group extensions of endomorphisms Jon Aaronson and Benjamin Weiss; 4. Lyapunov exponents with multiplicity 1 for deterministic products of matrices C. Bonnati and M. Viana; 5. Remarks on stability and diffusion in high-dimensional Hamiltonian systems and partial differential equations Jean Bourgain; 6. Stable manifolds and the Perron–Irwin method Marc Chaperon; 7. C2 densely the 2-sphere has an elliptic closed geodesic Gonzalo Contreras and Fernando Oliveira; 8. Further rigidity properties of conformal Anosov systems R. De La Lave; 9. On some approximation of the 3D Euler system E. I. Dinaburg and Ya G. Sinai; 10. Lyapunov 1-forms for flows M. Farber, T. Kappeler, J. Latschev and E. Zehnder; 11. Constructions in elliptic dynamics Bassam Fayad and Anatole Katok; 12. Démonstration du 'théorème d'Arnold' sur la stabilité du système planétaire (d'après Herman) Jacques Féjoz; 13. Sur le théorème de Bertrand (d'après Michael Herman) Jacques Féjoz and Laurent Kaczmarek; 14. Commutators and diffeomorphisms of surfaces Jean-Marc Gambaudo and Étienne Ghys; 15. Wandering domains and random walks in Gevrey near-integrable systems Jean-Pierre Marco and David Sauzin; 16. Examples of Aubry sets John N. Mather; 17. New phenomena associated with homoclinic tangencies Sheldon E. Newhouse; 18. On holomorphic critical quasi-circle maps Carsten Lunde Petersen; 19. KAM theorem for Gevrey Hamiltonians G. Popov; 20. Convergent transformations into a normal form in analytic Hamiltonian systems with two degrees of freedom on the zero energy surface near degenerate elliptic singularities Helmut Rüssmann; 21. Sur les structures de Poisson singulières Laurent Stolovitch.