# American Institute of Mathematical Sciences

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May  2010, 27(2): 787-798. doi: 10.3934/dcds.2010.27.787

## Omega-limit sets for spiral maps

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

Received  October 2009 Revised  February 2010 Published  February 2010

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.
Citation: Bruce Kitchens, Michał Misiurewicz. Omega-limit sets for spiral maps. Discrete & Continuous Dynamical Systems, 2010, 27 (2) : 787-798. doi: 10.3934/dcds.2010.27.787
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