Dynamical Systems

Abstract

We have developed a structure theory for real analytic diffeomorphisms of compact surfaces very similar to the well known structure theory of Axiom A diffeomorphisms. This theory has strong implications for the structure of systems with two degrees of freedom. We have also found a relatively simple proof of our previously established result that there are residual subsets A of open sets of diffeomorphisms with the property that each element in A has infinitely many sinks. Another result states that many systems with two degrees of freedom have fractal basin boundaries with Hausdorff dimension two (i.e. maximal Hausdorff dimension). This leads to the frequent existence of what we call pseudo-attractors -- closed invariant sets with dense orbits whose basins have maximal dimension. (edc)

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Document Details

Document Type
Technical Report
Publication Date
Dec 31, 1987
Accession Number
ADA215319

Entities

People

  • Sheldon E. Newhouse

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Air Force
  • Availability
  • Boundaries
  • Classification
  • Continuity
  • Monitoring
  • Notation
  • Procurement
  • Residuals
  • Scientific Research

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Space