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)
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