Robust attractors without dominated splitting on manifolds with boundary

Dante Carrasco-Olivera; Bernardo San Martín

doi:10.3934/dcds.2014.34.4555

Article Contents

2014, Volume 34, Issue 11: 4555-4563. Doi: 10.3934/dcds.2014.34.4555

This issue Previous Article Localization, smoothness, and convergence to equilibrium for a thin film equation Next Article On ill-posedness for the generalized BBM equation

Robust attractors without dominated splitting on manifolds with boundary

Dante Carrasco-Olivera^1, and
Bernardo San Martín^2,

1.
Departamento de Matemática, Universidad del Bío-Bío, Av. Collao 1202, Casilla 5-C, Concepción
2.
Departamento de Matemáticas, Universidad Católica del Norte, Av. Angamos 0610, Casilla 1280, Antofagasta

Received: August 2013

Revised: February 2014

Published: November 2014

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Abstract

In this paper we prove that there exists a positive integer $k$ with the following property: Every compact $3$-manifold with boundary carries a $C^\infty$ vector field exhibiting a $C^k$-robust attractor without dominated splitting in a robust sense.

Keywords:

Mathematics Subject Classification: Primary: 34D45, 37D30; Secondary: 37C10, 37F15, 37D99.

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