# 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

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topNassiri, 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 -

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