Thursday, November 5, 2015

resource recommendations - Self-study book for dynamical systems theory?



What textbook would you recommend for a bachelor in theoretical physics to study dynamical systems theory? I don't want to focus too much on chaos, just having a broad view of every interesting characteristic is enough. Physical meaning behinds equations should be explained.


Some related resources:




Answer



In no specific order:



  • Alligood K.T., Sauer T.D., Yorke J.A, Chaos. An Introduction to Dynamical Systems



That's a personal favorite of mine at the undergraduate level. It's clearly written and they strike a great physics/math balance, including from (a few) mathematical proofs to "computer experiments".



  • Tél T., Gruiz M., Chaotic dynamics. An introduction based on classical mechanics


Highly recommended. Also aimed the the undergraduate level, it's very clear conceptually and strives to make the math accessible. It's a newer book (2006) that includes current topics.



  • Ott E., Chaos in Dynamical Systems


A classic that cannot be missed. It's aimed at the graduate level, but it's pretty accessible and especially useful when you need to get to the details of some specific topic.




  • Strogatz S.H., Nonlinear Dynamics And Chaos: With Applications to Physics, Biology, Chemistry, and Engineering


It's explicitly aimed at newcomers and has only calculus and introductory physics as prerequisites. The title "applications" include "love affairs" as 2-D flows and, possibly very interesting, the author lectures are available on Youtube.



  • Cvitanović P., Artuso R., Mainieri R., Tanner G., and Vattay G., Chaos: Classical and Quantum $-$ ChaosBook.org


That's a very interesting freely available on-line graduate textbook. It takes a fresh approach to the subject and "aims to bridge the gap between the physics and mathematics dynamical systems literature".


No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...