# American Institute of Mathematical Sciences

January  2017, 37(1): 337-354. doi: 10.3934/dcds.2017014

## Finiteness and existence of attractors and repellers on sectional hyperbolic sets

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

* Corresponding author: A. M. López

Received  March 2015 Revised  September 2016 Published  November 2016

Fund Project: The author was supported by CAPES, Brazil.

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.

Citation: A. M. López. Finiteness and existence of attractors and repellers on sectional hyperbolic sets. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 337-354. doi: 10.3934/dcds.2017014
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##### References:
Three dimensional case. Cross-section
Four dimensional case. Cross-sections
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