EMPTY INTERIOR RECURRENCE FOR CONTINUOUS FLOWS ON SURFACES-Reference-Cited by-同舟云学术

EMPTY INTERIOR RECURRENCE FOR CONTINUOUS FLOWS ON SURFACES

Published:2010-09 Issue:09 Volume:20 Page:2897-2913
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

LÓPEZ VÍCTOR JIMÉNEZ¹,LÓPEZ GABRIEL SOLER²

Affiliation:

1. Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain

2. Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo Alfonso XIII 52, 30203 Cartagena, Spain

Abstract

In this paper we characterize topologically the empty interior subsets of a compact surface S which can be ω-limit sets of recurrent orbits (but not of nonrecurrent ones) of continuous flows on S. This culminates the classification of ω-limit sets for surface flows initiated in [Jiménez & Soler, 2001; Soler, 2003; Jiménez & Soler, 2004a, 2004b]. We also show that this type of ω-limit sets can always be realized (up to topological equivalence) by smooth flows but cannot be realized by analytic flows.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127410027441

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