One-Dimensional Dynamical Systems
An Example-Led Approach
1st Edition
Published on 11. August 2021
Book
Paperback/Softback
118 pages
978-0-367-70108-6 (ISBN)
Description
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 ? 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
Features
Example-driven approach
Suitable as supplementary reading for a graduate or advanced undergraduate course in dynamical systems
More details
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Illustrations
32 s/w Abbildungen, 32 s/w Zeichnungen
32 Line drawings, black and white; 32 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 7 mm
Weight
196 gr
ISBN-13
978-0-367-70108-6 (9780367701086)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
08/2021
1st Edition
Chapman & Hall/CRC
€185.30
Shipment within 15-20 days
E-Book
08/2021
1st Edition
Chapman & Hall/CRC
€68.49
Available for download
E-Book
08/2021
1st Edition
Chapman & Hall/CRC
€68.49
Available for download
Person
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).
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).
Content
1. Introduction. 2. Rotation Numbers. 2.1. Arnold Tongues for Double Standard Maps. 2.2 Arnold Tongues for ?-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 ?-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 ?-Standard Maps. Bibliography.