We prove a fixed point theorem for continuous mappings which satisfy a compression-expansion condition on the boundary of a N-dimensional cell of R^N. Our work is motivated by a previous theorem of Andres, Gaudenzi and Zanolin (1990) dealing with the existence of periodic solutions for dissipative-repulsive systems and is also related to some recent results by Zgliczyński and Gidea (2004) concerning covering relations for Markov partitions. Applications are given to the study of the iterates of a continuous map of R^N. In this case we obtain some theorems on the existence of periodic points and chaotic-like dynamics

Pireddu, M., Zanolin, F. (2005). Fixed points for dissipative-repulsive systems and topological dynamics of mappings defined on N-dimensional cells. ADVANCED NONLINEAR STUDIES, 5(3), 411-440 [10.1515/ans-2005-0306].

Fixed points for dissipative-repulsive systems and topological dynamics of mappings defined on N-dimensional cells

PIREDDU, MARINA;
2005

Abstract

We prove a fixed point theorem for continuous mappings which satisfy a compression-expansion condition on the boundary of a N-dimensional cell of R^N. Our work is motivated by a previous theorem of Andres, Gaudenzi and Zanolin (1990) dealing with the existence of periodic solutions for dissipative-repulsive systems and is also related to some recent results by Zgliczyński and Gidea (2004) concerning covering relations for Markov partitions. Applications are given to the study of the iterates of a continuous map of R^N. In this case we obtain some theorems on the existence of periodic points and chaotic-like dynamics
Articolo in rivista - Articolo scientifico
Fixed points, periodic points, homeomorphisms, Brouwer degree, rectangular cells, chaotic-like dynamics, topological horseshoes.
English
2005
5
3
411
440
none
Pireddu, M., Zanolin, F. (2005). Fixed points for dissipative-repulsive systems and topological dynamics of mappings defined on N-dimensional cells. ADVANCED NONLINEAR STUDIES, 5(3), 411-440 [10.1515/ans-2005-0306].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/46079
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