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Geometry and Topology in Dynamics
Edited by: Marcy Barge, Montana State University, Bozeman, MT, and Krystyna Kuperberg, Auburn University, AL
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Contemporary Mathematics
1999; 252 pp; softcover
Volume: 246
ISBN-10: 0-8218-1958-5
ISBN-13: 978-0-8218-1958-6
List Price: US$68
Member Price: US$54.40
Order Code: CONM/246
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This volume consists of the written presentations of lectures given at two special sessions: the AMS Special Session on Topology in Dynamics (Winston-Salem, NC) and the AMS-AWM Special Session on Geometry in Dynamics (San Antonio, TX). Each article concerns aspects of the topology or geometry of dynamical systems. Topics covered include the following: foliations and laminations, iterated function systems, the three-body problem, isotopy stability, homoclinic tangles, fractal dimension, Morse homology, knotted orbits, inverse limits, contact structures, Grassmanians, blowups, and continua.

New results are presented reflecting current trends in topological aspects of dynamical systems. The book offers a wide variety of topics of special interest to those working this area bridging topology and dynamical systems.

Readership

Graduate students and research mathematicians interested in analysis; physicists.Graduate students and research mathematicians interested in analysis; physicists.

Table of Contents

  • M. Barge, J. Jacklitch, and G. Vago -- Homeomorphisms of one-dimensional inverse limits with applications to substitution tilings, unstable manifolds, and tent maps
  • P. Boyland -- Isotopy stability of dynamics on surfaces
  • H. Bruin -- Homeomorphic restrictions of unimodal maps
  • A. Clark -- Flows on solenoids are generically not almost periodic
  • P. Collins -- Dynamics forced by surface trellises
  • P. Duvall and J. Keesling -- The Hausdorff dimension of the boundary of the Lévy dragon
  • J. B. Etnyre and R. W. Ghrist -- Stratified integrals and unknots in inviscid flows
  • V. L. Ginzburg and E. Kerman -- Periodic orbits in magnetic fields in dimensions greater than two
  • P. Hanus and M. Urbański -- A new class of positive recurrent functions
  • A. Illanes, S. Macías, and S. B. Nadler, Jr. -- Symmetric products and \(Q\)-manifolds
  • S. R. Kaplan -- Symbolic dynamics of the collinear three-body problem
  • A. Kasman -- Grassmannians, nonlinear wave equations and generalized Schur functions
  • J. E. Keesling and C. Krishnamurthi -- The similarity boundary of a self-similar set
  • P. Minc -- Homotopy classes of maps between Knaster continua
  • M. Schwarz -- Equivalences for Morse homology
  • C. R. Seaquist -- More monotone open homogeneous locally connected plane continua
  • C. W. Stark -- Blowup and fixed points
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