# 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:

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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".

• Thanks. But why are all of them about chaos? – Ooker Sep 2 '17 at 16:12
• @Ooker, to some degree it's my own bias, since that's my field of research. But I believe that complex systems (chaos) is also the branch of physics that most regularly uses the concept of fractals, as it comes about quite often: in the boundary between phase space regions that correspond to different behaviors ("basins of attraction") and in the typical geometry of chaotic attractors, for instance. – stafusa Sep 2 '17 at 19:10
• But as I understand from the book Complexity: A Guided Tour, complex system science does not completely deal with chaos, and it's an interdisciplinary field, not just a branch of physics. And while dynamical system theory originated from the three-body problem, it's actually a branch of mathematics, and its scope surely is broader than just chaos? Please correct me if I'm wrong. – Ooker Sep 3 '17 at 16:26
• @Ooker, oh, ok, that part of the comment is indeed misleading. The definitions are pretty vague, but usually "complex system" is the biggest category, with most of "dynamical systems" in it, together with networks, emergence, etc. And, "dynamical systems", even as done by physicists, includes more than chaos: e.g., bifurcation theory and even linear systems, but I think chaos is the most common research subject. – stafusa Sep 3 '17 at 19:43
• Fluids are complex systems, no doubt, and advection of particles, even in a periodic flow can be chaotic. Lagrangian is actually the formalism I've seen the least being used. While the Hamiltonian formalism dominates the description of conservative systems, usually the Newtonian mechanics is used to describe a forced pendulum or an engineering model. The field of dynamical systems only cares about the behavior of the system - which formalism one employs to obtain the equations of motion (or whether it's a mechanical system at all) is secondary. – stafusa Sep 4 '17 at 15:35