Robustly transitive behavior in symplectic dynamics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866916016095756288 |
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| author | Paradela, Jaime |
| author_facet | Paradela, Jaime |
| contents | We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a domination condition we show that a broad class of real-analytic deformations of this system display large robustly transitive sets. As a corollary of our construction we also obtain new examples of real-analytic robustly transitive symplectomorphisms which are not uniformly hyperbolic.
To establish these results we develop perturbation techniques to create blender horseshoes in the real-analytic setting and import ideas from control theory which show that, typically, these objects have a large domain of influence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15922 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robustly transitive behavior in symplectic dynamics Paradela, Jaime Dynamical Systems We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a domination condition we show that a broad class of real-analytic deformations of this system display large robustly transitive sets. As a corollary of our construction we also obtain new examples of real-analytic robustly transitive symplectomorphisms which are not uniformly hyperbolic. To establish these results we develop perturbation techniques to create blender horseshoes in the real-analytic setting and import ideas from control theory which show that, typically, these objects have a large domain of influence. |
| title | Robustly transitive behavior in symplectic dynamics |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.15922 |