Robustly transitive behavior in symplectic dynamics
Dynamical Systems
2026-05-18 v1
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.
Cite
@article{arxiv.2605.15922,
title = {Robustly transitive behavior in symplectic dynamics},
author = {Jaime Paradela},
journal= {arXiv preprint arXiv:2605.15922},
year = {2026}
}