Based on the conference/workshop on Continuum Theory and Dynamical Systems held in Lafayette, Louisiana, this reference illustrates the current expansion of knowledge on the relationship between these subjects. It presents new problems in hyperspaces, induced maps, universal maps, fixed-point sets, disconnected numbers and quotient maps.;Explaining the definitions and techniques used in the two fields and providing results from both areas, this volume: examines prime end (accessible) rotation numbers for chaotic sets and Henon maps; discussed the connection between the rotation shadowing property and the structure of the rotation set for annulus homeomorphisms; offers a Nielson-type theorum concerning the minimum number of fixed points for an area preserving homeomorphism of the two disc; constructs a closed unit disc that admits many inequivalent homeomorphisms that are Denjoy on the boundary and distinct irrational rotations on the interior; gives a geometric description of a horseshoe-type mapping of a plane disc into itself whose attracting set is not chainable; and considers semigroups generated by maps topologically conjugate to contractions.;Written by experts who provide a cross-disciplinary perspective, this volume is intended for applied mathematicians, topologists, geomesters, physicists and graduate-level students in these disciplines.
Table of Contents
Accessible Rotation Numbers for Chaotic States, Kathleen T. Alligood and Timothy Sauer Prime End Rotation Numbers Associated with the Henon Maps, Marcy Barge On the Rotation Shadowing property for Annulus Maps, Fernanda Botelho and Liang Chen A Nielsen-Type Theorem for Area-Preserving Homeomorphisms of the Two Disc, Kenneth Boucher, Morton Brown, and Edward Slaminka Irrational Rotations on Simply Connected Domains, Beverly L. Brechner The Rotational Dynamics of Cofrontiers, Beverly L. Brechner, Merle D. Guay, and John C. Mayer A periodic Homeomorphism of the Plane, Morton Brown Dynamical Connections Between a Continuous Map and Its Inverse Limit Space, Liang Chen and Shihai Li Horseshoelike Mappings and Chainability James F Davis Iterated Function Systems, Compact Semigroups, and Topological Contractions, P F Duvall ,Jr.,John Wesley Emert, and Lawrence, S. Husch The Forced Damped Pendulum and the Wada Property, Judy Kennedy and James A. Yorke Denjoy Meets Rotation on an Indecomposable Cofrontier, John C. Mayeer and Lex G. Oversteegen New problems in Continuum Theory, Sam B. Nadler, Jr. A Continuum Separated by Each of Its Nondegenerate Proper Subcontinua, Sam B.Nadler Jr., and Gary A. Seldomridge. Dense Embeddings into Cubes and Manifolds, J. Nikiel, H M. Tuncali, and E. D. Tymchatyn An Example Concerning Disconnection Numbers, Robert Pierce Indecomposable Continua, Prime Ends, and Julia Sets, James T Rogers, Jr. Homeomorphisms on Cofrontiers with Unique Potation Number, Mark H .Turpin.