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Open Access

Fixed points, periodic points, and coin-tossing sequences for mappings defined on two-dimensional cells

Fixed Point Theory and Applications20042004:126568

Received: 12 January 2004

Published: 7 June 2004


We propose, in the general setting of topological spaces, a definition of two-dimensional oriented cell and consider maps which possess a property of stretching along the paths with respect to oriented cells. For these maps, we prove some theorems on the existence of fixed points, periodic points, and sequences of iterates which are chaotic in a suitable manner. Our results, motivated by the study of the Poincaré map associated to some nonlinear Hill's equations, extend and improve some recent work. The proofs are elementary in the sense that only well known properties of planar sets and maps and a two-dimensional equivalent version of the Brouwer fixed point theorem are used.

Authors’ Affiliations

Dipartimento dell'Ingegneria dell'Informazione, Università di Siena, Siena, Italy
Dipartimento di Matematica e Informatica, Università di Udine, Udine, Italy


© Papini and Zanolin 2004