Work

High-order homoclinic tangencies of corank 2

Year: 2025

Type: article

Abstract: We prove that in the space of $C^r$ maps $(r=2,\ldots ,\infty ,\omega )$ of a smooth manifold of dimension at least 4, there exist open regions where maps with infinitely many corank-2 homoclinic tangencies of all orders are dense. The result is applied to show the existence of maps with universal two-dimensional dynamics, that is, maps whose iterations approximate the dynamics of every map of a two-dimensional disk with an arbitrarily good accuracy. We show that maps with universal two-dimensional dynamics are $C^r$ -generic in the regions under consideration.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2025.10209

Author: DMITRII MINTS

Institutions: National Research University Higher School of Economics, Imperial College London

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Leverhulme Trust, Russian Science Foundation