A note on the coding of orbits in certain discontinuous maps

• Type: Article in International Scientific Journal
• Date: 2010

Authors

M. Mendes (Author) FEUP

Journal

Title: Discrete and Continuous Dynamical Systems

Vol. 27 No. 1

Pages: 369-382

ISSN: 1078-0947

Publisher: American Institute of Mathematical Sciences

Indexing

ISI Web of Science

Scopus

Scientific classification

FOS: Natural sciences > Mathematics

CORDIS: Physical sciences > Mathematics > Chaos theory

Other information

DOI: 10.3934/dcds.2010.27.369

Abstract (EN): We study certain discontinuous maps by means of a coding map defined on a special partition of the phase space which is such that the points of discontinuity of the map, D, all belong to the union of the boundaries of elements in the partition. For maps acting locally as homeomorphisms in a compact space, we prove that, if the set of points whose trajectory comes arbitrarily close to the set of discontinuities is closed and not the full space then all points not in that set are rationally coded, i.e., their codings eventually settle on a repeated block of symbols. In particular, for piecewise isometries, which are discontinuous maps acting locally as isometries, we give a topological description of the equivalence classes of the coding map in terms of the connected components generated by the closure of the preimages of D.

Language: English

Type (Professor's evaluation): Scientific