Finiteness and existence of attractors and repellers on sectional hyperbolic sets

A. M. López

doi:10.3934/dcds.2017014

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2017, Volume 37, Issue 1: 337-354. Doi: 10.3934/dcds.2017014

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Finiteness and existence of attractors and repellers on sectional hyperbolic sets

A. M. López^,

Instituto de Ciências Exatas (ICE), Universidade Federal Rural do Rio de Janeiro, 23890-000 Seropédica, Rio de Janeiro, Brazil

* Corresponding author: A. M. López
* Corresponding author: A. M. López

Received: March 2015

Revised: September 2016

Published: September 2017

The author was supported by CAPES, Brazil.

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Abstract

We study small perturbations of a sectional hyperbolic set of a vector field on a compact manifold. Indeed, we obtain an upper bound for the number of attractors and repellers that can arise from these perturbations. Moreover, no repeller can arise if the unperturbed set has singularities, is connected and consists of nonwandering points.

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Mathematics Subject Classification: Primary:37D30, 37D45, 37D50;Secondary:37D25.

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Figure 1. Three dimensional case. Cross-section

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Figure 2. Four dimensional case. Cross-sections

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