Robust Transitivity in Hamiltonian Dynamics
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2011
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| _version_ | 1866913479274790912 |
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| author | Nassiri, Meysam Pujals, Enrique R. |
| author_facet | Nassiri, Meysam Pujals, Enrique R. |
| contents | 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 ($r=1, 2, ..., \infty$) of symplectic diffeomorphisms and Hamiltonian systems, exhibiting "large" robustly transitive sets. We show that the $C^\infty$ closure of such open sets contains a variety of systems, including so-called a 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1108_6012 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Robust Transitivity in Hamiltonian Dynamics Nassiri, Meysam Pujals, Enrique R. Dynamical Systems Mathematical Physics Symplectic Geometry 37D30, 37J40 (Primary) 53Dxx, 70Fxx, 70Hxx (Secondary) 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 ($r=1, 2, ..., \infty$) of symplectic diffeomorphisms and Hamiltonian systems, exhibiting "large" robustly transitive sets. We show that the $C^\infty$ closure of such open sets contains a variety of systems, including so-called a 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. |
| title | Robust Transitivity in Hamiltonian Dynamics |
| topic | Dynamical Systems Mathematical Physics Symplectic Geometry 37D30, 37J40 (Primary) 53Dxx, 70Fxx, 70Hxx (Secondary) |
| url | https://arxiv.org/abs/1108.6012 |