One-Dimensional Dynamical Systems: An Example-Led Approach

✍ Scribed by Ana Rodrigues

Publisher: CRC Press
Year: 2021
Tongue: English
Leaves: 119
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

For almost every phenomenon in physics, chemistry, biology, medicine, economics, and other sciences, one can make a mathematical model that can be regarded as a dynamical system.
One-Dimensional Dynamical Systems: An Example-Led Approach
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.

Features

Example-driven approach

Suitable as supplementary reading for a graduate or advanced undergraduate course in dynamical systems

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Contents
Chapter 1: Introduction
Chapter 2: Rotation numbers
2.1. ARNOLD TONGUES FOR DOUBLE STANDARD MAPS
2.2. ARNOLD TONGUES FOR a-STANDARD MAPS
Chapter 3: Topological conjugacy
Chapter 4: Critical points
Chapter 5: Topological theory of chaos
5.1. TOPOLOGICAL ENTROPY
5.2. SCHWARZIAN DERIVATIVE
Chapter 6: Symbolic dynamics
6.1. KNEADING SEQUENCES FOR DOUBLE STANDARD MAPS
6.2. KNEADING SEQUENCES FOR a STANDARD MAPS
Chapter 7: Tongues
7.1. LENGTH OF TONGUES
7.2. BOUNDARY OF THE TONGUES
7.3. TIP OF THE TONGUES
7.3.1 Applications of Theorem 7.3.2 to double standard maps
7.4. CONNECTEDNESS OF TONGUES
7.5. ARNOLD TONGUES OF HIGHER PERIODS FOR a-STANDARD MAPS
Bibliography
Index

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