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Robustly transitive behavior in symplectic dynamics

  • Jaime Paradela
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Abstract

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 local domination condition we show that a typical real-analytic deformations of this system display large robustly transitive sets. As a corollary of our construction we also obtain new open sets of real-analytic symplectomorphisms which are topologically mixing but 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.

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Cite

BibTeXRIS
BibTeX
@misc{paradela2026robustly,
  title = {{Robustly transitive behavior in symplectic dynamics}},
  author = {Jaime Paradela},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.15922},
  eprint = {2605.15922},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.15922},
}
RIS
TY  - UNPB
TI  - Robustly transitive behavior in symplectic dynamics
AU  - Jaime Paradela
PY  - 2026
DA  - 2026/10/31
PB  - arXiv
DO  - 10.48550/arxiv.2605.15922
UR  - https://arxiv.org/abs/2605.15922
AB  - 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 local domination condition we show that a typical real-analytic deformations of this system display large robustly transitive sets. As a corollary of our construction we also obtain new open sets of real-analytic symplectomorphisms which are topologically mixing but 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.
ER  -