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.
- Example-driven approach
- Suitable as supplementary reading for a graduate or advanced undergraduate course in dynamical systems
Table of Contents
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.
Ana Rodrigues is an associate professor in the Mathematics Department, University of Exeter. She earned her PhD in mathematics in dynamical systems in 2007 from the University of Porto.
Before arriving at Exeter, she was a postdoc at Indiana University Purdue University at Indianapolis, USA, for two years and then held a research assistant position at KTH - Royal Institute of Technology and Uppsala University, Sweden, financed by the Swedish Research Council.
Her research interests are in dynamical systems (low-dimensional dynamical systems, ergodic theory, limit cycles of differential equations and dynamical systems with symmetry).