Homoclinic tangency of codimension 2 and historic wandering domains
Abstract
We construct a four-dimensional diffeomorphism exhibiting a homoclinic tangency of the largest codimension, which admits a historic wandering domain of positive Lebesgue measure. Every orbit in this wandering domain exhibits historic behavior, in the sense that time averages do not converge. This example shows that homoclinic tangencies of the largest codimension can still give rise to positive Lebesgue measure sets with non-convergent statistical behavior.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Quantum chaos and dynamical systems
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 16 February 2026
- Language
- EN
- Document type
- Preprint