Theoretical Investigations of Chaotic Dynamics
Abstract
One of the outstanding problems of chaotic dynamics has been to show that chaos develops monotonically as the parameter is varied, for some systems. Results along this line have been very few. An overview of these results has been given in the proposal for this funding period. Kan and Yorke have discovered results in two dimensions which clearly indicate the situation is far worse than previously believed. Their results require some mild nondegeneracy conditions which shall not be spelled out in detail here. Their results are for diffeomorphisms that depend on a parameter. They show that monotonicity never occurs in two dimensions as the parameter varies, except in the most trivial situations. In (KY) these results have been written for a specical prototype example which seems quite typical. This example has nice simple choices of coordinates, and analysis is facilitated. Establishment of the full result was much more difficult and the analysis has been carried out in (KKY).
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1991
- Accession Number
- ADA241790
Entities
People
- James Yorke
Organizations
- University of Maryland