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SumTopo 2001, Sixteenth Summer Conference on Topology and its Applications
July 18-21, 2001
City College of CUNY
New York, NY, USA

Organizers
Ralph Kopperman (City College, CUNY), Susan Andima (CW Post College, LIU), Gerald Itzkowitz (Queens College, CUNY), Prabudh Misra (College of Staten Island, CUNY), Shelly Rothman (CW Post College, LIU), Aaron Todd (Baruch College, CUNY)

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Problems with the definition of the C0 UPOTP.
by
Marcin Kulczycki
Auburn University, Jagiellonian University

A discrete dynamical system on a manifold has the uniform pseudo-orbit tracing property (or UPOTP), if there is a neighbourhood of this system in the space of self-mappings of this manifold such that all mappings from this neighbourhood have the pseudo-orbit tracing property (i.e. pseudo-orbits can be traced by orbits as closely as we wish, if we choose sufficiently small jump for the pseudo-orbit) and constants for POTP can be defined globally on this neighbourhood.

In 1997 UPOTP (previously studied for diffeomorphisms of smooth manifolds) was defined by R.Gu for continuous mappings of topological manifolds. However, UPOTP treated this way is too general - we show that for nearly all manifolds no continuous mapping of this manifold onto itself has this property.

Date received: May 19, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-68.