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Stable Index Pairs for Discrete Dynamical Systems

Published online by Cambridge University Press:  20 November 2018

Tomasz Kaczynski
Affiliation:
Département de mathématiques et d’informatique, Sherbrooke, Québec, J1K 2R1, kaczyn@.usherb.ca
Marian Mrozek
Affiliation:
Instytut Informatyki, Uniwersytet Jagiellónski, PL-30-072 Kraków, Poland, mrozek@.uj.edu.pl
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Abstract

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A new shorter proof of the existence of index pairs for discrete dynamical systems is given. Moreover, the index pairs defined in that proof are stable with respect to small perturbations of the generating map. The existence of stable index pairs was previously known in the case of diffeomorphisms and flows generated by smooth vector fields but it was an open question in the general discrete case.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1997

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