Topological entropy for set-valued maps

Dante  Carrasco-Olivera; Roger Metzger  Alvan; Carlos Arnoldo Morales  Rojas

doi:10.3934/dcdsb.2015.20.3461

Article Contents

2015, Volume 20, Issue 10: 3461-3474. Doi: 10.3934/dcdsb.2015.20.3461

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Topological entropy for set-valued maps

1.
Departamento de Matemática, Universidad del Bío, Bío Av. Collao # 1202, Casilla 5-C, VIII-Región, Concepción
2.
Instituto de Matemática y Ciencias Afines (IMCA), Universidad Nacional de Ingeniería, Calle Los Biólogos 245, Urb. San César La Molina, Lima 12, Lima
3.
Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro

Received: April 2015

Revised: May 2015

Published: December 2015

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Abstract

In this paper we define and study the topological entropy of a set-valued dynamical system. Actually, we obtain two entropies based on separated and spanning sets. Some properties of these entropies resembling the single-valued case will be obtained.

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Mathematics Subject Classification: Primary: 37B40; Secondary: 54C60.

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