Omega-limit sets for spiral maps

Bruce Kitchens; Michał Misiurewicz

doi:10.3934/dcds.2010.27.787

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2010, Volume 27, Issue 2: 787-798. Doi: 10.3934/dcds.2010.27.787

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Omega-limit sets for spiral maps

Bruce Kitchens^1, and
Michał Misiurewicz^1,

1.
Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202

Received: September 30, 2009

Revised: January 31, 2010

Published: June 2010

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Abstract

We investigate a class of homeomorphisms of a cylinder, with all trajectories convergent to the cylinder base and one fixed point in the base. Let A be a nonempty finite or countable family of sets, each of which can be a priori an $\omega$-limit set. Then there is a homeomorphism from our class, for which A is the family of all $\omega$-limit sets.

Keywords:

$\omega$-limit set.

Mathematics Subject Classification: 37B99.

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