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

chapter Chapter 1|4 pages


chapter Chapter 2|32 pages

Rotation numbers

chapter Chapter 3|4 pages

Topological conjugacy

chapter Chapter 4|10 pages

Critical points

chapter Chapter 5|16 pages

Topological theory of chaos

chapter Chapter 6|22 pages

Symbolic dynamics

chapter Chapter 7|18 pages