Robust transitivity in hamiltonian dynamics

Meysam Nassiri; Enrique R. Pujals

Annales scientifiques de l'École Normale Supérieure (2012)

  • Volume: 45, Issue: 2, page 191-239
  • ISSN: 0012-9593

Abstract

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A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce C r open sets ( r = 1 , 2 , ⋯ , ∞ ) of symplectic diffeomorphisms and Hamiltonian systems, exhibitinglargerobustly transitive sets. We show that the C ∞ closure of such open sets contains a variety of systems, including so-calleda priori unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of the proof is a combination of studying minimal dynamics of symplectic iterated function systems and a new tool in Hamiltonian dynamics which we call “symplectic blender”.

How to cite

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Nassiri, Meysam, and Pujals, Enrique R.. "Robust transitivity in hamiltonian dynamics." Annales scientifiques de l'École Normale Supérieure 45.2 (2012): 191-239. <http://eudml.org/doc/272173>.

@article{Nassiri2012,
abstract = {A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce $C^\{r\}$ open sets ($r=1, 2, \dots , \infty $) of symplectic diffeomorphisms and Hamiltonian systems, exhibitinglargerobustly transitive sets. We show that the $C^\{\infty \}$ closure of such open sets contains a variety of systems, including so-calleda priori unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of the proof is a combination of studying minimal dynamics of symplectic iterated function systems and a new tool in Hamiltonian dynamics which we call “symplectic blender”.},
author = {Nassiri, Meysam, Pujals, Enrique R.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {symplectic blender; robust transitivity; hamiltonian dynamics; instability problem},
language = {eng},
number = {2},
pages = {191-239},
publisher = {Société mathématique de France},
title = {Robust transitivity in hamiltonian dynamics},
url = {http://eudml.org/doc/272173},
volume = {45},
year = {2012},
}

TY - JOUR
AU - Nassiri, Meysam
AU - Pujals, Enrique R.
TI - Robust transitivity in hamiltonian dynamics
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2012
PB - Société mathématique de France
VL - 45
IS - 2
SP - 191
EP - 239
AB - A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce $C^{r}$ open sets ($r=1, 2, \dots , \infty $) of symplectic diffeomorphisms and Hamiltonian systems, exhibitinglargerobustly transitive sets. We show that the $C^{\infty }$ closure of such open sets contains a variety of systems, including so-calleda priori unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of the proof is a combination of studying minimal dynamics of symplectic iterated function systems and a new tool in Hamiltonian dynamics which we call “symplectic blender”.
LA - eng
KW - symplectic blender; robust transitivity; hamiltonian dynamics; instability problem
UR - http://eudml.org/doc/272173
ER -

References

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