Introduction to applied nonlinear dynamical systems and chaos

Name: Introduction to applied nonlinear dynamical systems and chaos
ISBN: 9780387001777

Stephen Wiggins · 1990

This significant volume is intended for advanced undergraduate or first year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas which will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry and biology, will find this text as useful as students of mathematics. Overall, this will be a text that should be required for all students entering this field.

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lanstinAug 2023
These systems do not have periodic orbits they have symmetric strange attractors.
So tracing a particle thru these systems will not result in periodicity but will trace out these symmetric structures. It is unclear from the website if these are proven symmetries or observed.
A good book that is a bit more technical than Gleick (which I found not wrong in the details it does have) is “Introduction to Applied Nonlinear Dynamical Systems and Chaos” by Stephen Wiggins. It requires basic under grad maths but is a graduate text in that very close reading is needed to follow. The first 17 chapters are intended as a semester class.
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lotharbotJul 2013
My favorite surprising result in mathematics is that you can create chaos in the mathematical sense [1] with a bi-infinite binary sequence and the bitshift operation. Essentially, "multiplying by two" is chaotic in the right circumstances.
The technical description can be found starting at page 567 of [0], though the Google Books preview has some important pages missing.
[0] Stephen Wiggins - Introduction to Applied Nonlinear Dynamical Systems and Chaos http://books.google.com/books?id=GYcOfuZDOKMC&lpg=PA565&ots=...
[1] The key attributes of chaos are described in http://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics
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