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arXiv · 2603.20830

Symplectic blenders near whiskered tori and persistence of saddle-center homoclinics

Dongchen Li·Dmitry Turaev
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Abstract

A blender is a hyperbolic basic set such that the projection of its stable/unstable set onto some center subspace has a higher topological dimension than the set itself. We prove that, for any $C^s$ symplectic diffeomorphism (where $s=2,\dots\infty,\omega$), if it has a one-dimensional whiskered torus with a homoclinic orbit, then a symplectic blender can be created by an arbitrarily $C^s$-small perturbation. Using this result, we show that the non-transverse homoclinic intersection between the invariant manifolds of a saddle-center periodic point is persistent, in the sense that the original system lies in the $C^s$-closure of a $C^1$-open set of symplectic diffeomorphisms where those having saddle-center homoclinics are dense. Our results also hold in the corresponding continuous-time settings.

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Dongchen Li, Dmitry Turaev. 2026-03-21. Symplectic blenders near whiskered tori and persistence of saddle-center homoclinics. https://arxiv.org/abs/2603.20830

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