Recommendation for a book and other material on dynamical systems

I currently have the book Dynamical Systems with Applications Using Mathematica by Stephen Lynch. I used it in an undergrad introductory course for dynamical systems, but it’s extremely terse. As an example, one section of the book dropped the term ‘manifold’ at one point without giving a definition for the term. This is only one example; the rest of the book is similarly sparse on information.

I have a background in applied mathematics and computer science. If it’s necessary to cover some pre-requisite topics to get a good grasp of the subject (eg, topology, abstract algebra, etc), please feel free to mention this.

I’d love it if there were some pre-recorded lectures on the topic, but I’m not holding my breath. I’m looking for a book satisfying the following:

  • Needs to be readable without PhD level experience, for self study
  • Should cover both continuous and discrete dynamical systems
  • Bifurcation theory, lyapunov functions, manifolds, etc
  • My goal is to be able to understand more advanced treatments of the topic, but I don’t have an immense amount of free time. Among my frustrations with studying this particular topic is the material is so dense I spend a great deal of time trying to decipher terse phrases that turn out to be rather straightforward, just written cryptically.

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Nonlinear Dynamics and Chaos by Steven Strogatz is a great introductory text for dynamical systems. The writing style is somewhat informal, and the perspective is very “applied.” It includes topics from bifurcation theory, continuous and discrete dynamical systems, Liapunov functions, etc. and is very readable.

If you’re looking for something a little more advanced, some suggestions would be Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations by Paul Glendinning or Introduction to Applied Nonlinear Dynamical Systems and Chaos by Stephen Wiggins. These two texts include all of the topics above, along with much more discussion about manifolds and their stability.

The gratest mathematical book I have ever read happen to be on the topic of discrete dynamical systems and this is A “First Course in Discrete Dynamical Systems” Holmgren. This books is so easy to read that it feels like very light and extremly interesting novel. Topics introduced by Holmgren made me see mathematics in entirely new light and be happy as a child when he discover something new.

“An Introduction to Chaotic Dynamical Systems” is the one I prefer