Robustly transitive behavior in symplectic dynamics

Jaime Paradela

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arXiv · 2605.15922

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 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.

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BibTeX RIS

Jaime Paradela. 2026-05-15. Robustly transitive behavior in symplectic dynamics. https://arxiv.org/abs/2605.15922

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