The Hopf Bifurcation and Its Applications
by J. E. Marsden, M. McCracken
Publisher: Springer 1976
Number of pages: 424
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.
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by Nils Berglund - arXiv
This text is a slightly edited version of lecture notes for a course to undergraduate Mathematics and Physics students. Contents: Examples of Dynamical Systems; Stationary and Periodic Solutions; Local Bifurcations; Introduction to Chaotic Dynamics.
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We review some basic notions in ergodic theory and thermodynamic formalism, as well as introductory results in the context of max-plus algebra, in order to exhibit some properties of equilibrium measures when temperature goes to zero.
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A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules.