Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Paradela, Jaime
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161578633