Invitation to Dynamical Systems
by Edward R. Scheinerman
Publisher: Prentice Hall College Div 2000
Number of pages: 384
With this unique book, Scheinerman invites readers from a wide range of backgrounds with limited technical prerequisites to explore the beauty and excitement of dynamical systems in particular, and of mathematics in general. The book is designed for readers who want to continue exploring mathematics beyond linear algebra, but are not ready for highly abstract material. Rather than taking a standard mathematical theorem-proof-corollary-remark approach to dynamical systems, it stresses the intuition, ideology, and appreciation that is open to everyone.
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by J. E. Marsden, M. McCracken - Springer
The goal of these notes is to give a reasonably complete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to specific problems, including stability calculations.
by Alexander N. Gorban - American Mathematical Society
This monograph presents a systematic analysis of the singularities in the transition processes for dynamical systems. We study general dynamical systems, with dependence on a parameter, and construct relaxation times that depend on three variables.
by Roland K. W. Roeder - arXiv
We introduce the exciting field of complex dynamics at an undergraduate level while reviewing, reinforcing, and extending the ideas learned in an typical first course on complex analysis. Julia sets and the famous Mandelbrot set will be introduced...
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With a good background in nonlinear dynamics, chaos theory, and applications, the authors give a treatment of the basic principles of nonlinear dynamics in different fields. In addition, they show overlap with the traditional field of control theory.