Two problems in iterative nonlinear maps

This thesis consists of two parts. In the first part we study the dynamics and the boundaries between basins of attraction of a logistic map defined in real 2 x 2 matrices. We show how these boundaries are of a mixed type, combining fractal and smooth regions. We find in these boundaries a very complex distribution of transient scaling behaviors that can mask in some regions the fractal nature of the set. We propose a mechanism for the origin of these arbitrarily large transients in the scaling laws.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Perez, Gabriel

Contributors dc:contributor

• Chang, Shau-Jin

• Statistics
• Physics, General

Statement dc:rights

• Copyright 1990 Perez, Gabriel

Language dc:language

eng

Identifier

AAI9114371
(UMI)AAI9114371

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/21923