Dynamical Systems

by Edited by Albert Fathi , J.-C. Yoccoz

• ISBN13: 9780521860680
• ISBN10: 0521860687
• Format: Hardcover
• Copyright: 2006-03-06
• Publisher: Cambridge University Press

Summary

Michael Robert Herman had a profound impact on the theory of dynamical systems over the last 30 years. His seminar at the École 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.

Table of Contents

Michael Robert Herman, 1942--2000	3	(4)
Fathi, A.
Yoccoz, J.-C.
L2 regularity of measurable solutions of a finite-difference equation of the circle	7	(6)
Herman, M. R.
On Herman's theorem for ergodic, amenable group extensions of endomorphisms	13	(12)
Aaronson, J.
Weiss, B.
Lyapunov exponents with multiplicity 1 for deterministic products of matrices	25	(36)
Bonatti, C.
Viana, M.
Remarks on stability and diffusion in high-dimensional Hamiltonian systems and partial differential equations	61	(28)
Bourgain, J.
Stable manifolds and the Perron-Irwin method	89	(36)
Chaperon, M.
C2 densely the 2-sphere has an elliptic closed geodesic	125	(30)
Contreras, G.
Oliveira, F.
Further rigidity properties of conformal Anosov systems	155	(18)
de la Llave, R.
On some approximation of the 3D Euler system	173	(8)
Dinaburg, E. I.
Sinai, Ya G.
Lyapunov 1-forms for flows	181	(26)
Farber, M.
Kappeler, T.
Latschev, J.
Zehnder, E.
Constructions in elliptic dynamics	207	(44)
Fayad, B.
Katok, A.
Demonstration du `theoreme d'Arnold' sur la stabilite du systeme planetaire (d'apres Herman)	251	(62)
Fejoz, J.
Sur le theoreme de Bertrand (d'apres Michael Herman)	313	(8)
Fejoz, J.
Kaczmarek, L.
Commutators and diffeomorphisms of surfaces	321	(28)
Gambaudo, J.-M.
Ghys, E.
Wandering domains and random walks in Gevrey near-integrable systems	349	(48)
Marco, J.-P.
Sauzin, D.
Examples of Aubry sets	397	(58)
Mather, J. N.
New phenomena associated with homoclinic tangencies	455	(14)
Newhouse, S. E.
On holomorphic critical quasi-circle maps	469	(14)
Petersen, C. L.
KAM theorem for Gevrey Hamiltonians	483	(34)
Popov, G.
Convergent transformations into a normal form in analytic Hamiltonian systems with two degrees of freedom on the zero energy surface near degenerate elliptic singularities	517	(46)
Russman, H.
Sur les structures de Poisson singulieres	563	(32)
Stolovitch, L.
A remark on Stable manifolds and the Perron-Irwin method	595
Chaperon, M.