One-Dimensional Dynamical Systems: An Example-Led Approach

ISBN-13: 9780367701086 / Angielski / Miękka / 2021 / 112 str.

Ana Rodrigues

Opis

For almost every phenomenon in Physics, Chemistry, and other sciences one can make a mathematical model that can be regarded as a dynamical system. This book seeks to deep-dive into α standard maps as an example-driven way of explaining the modern theory of the subject in a way that will be engaging for students.

 

Spis treści

1. Introduction. 2. Rotation Numbers. 2.1. Arnold Tongues for Double Standard Maps. 2.2 Arnold Tongues for ɑ-Standard Maps. 3. Topological conjugacy. 4. Critical points. 5. Topological theory of Chaos. 5.1. Topological Entropy. 5.2. Schwarzian Derivative. 6. Symbolic Dynamics. 6.1. Kneading Sequences for Double Standard Maps. 6.2 Kneading Sequences for ɑ-Standard Maps. 7. Tongues. 7.1. Length of Tongues. 7.2. Boundary of The Tongues. 7.3. Tip of the Tongues. 7.4. Connectedness of Tongues. 7.5. Arnold Tongues of Higher Periods for ɑ-Standard Maps. Bibliography.