Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds. The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.
This is a book on nonlinear dynamical systems and their bifurcations under parameter variation.
This book deals with the theory of Poincaré--Birkhoff normal forms, studying symmetric systems in particular. Attention is focused on general Lie point symmetries, and not just on symmetries acting linearly.
D. Ruelle, Elements of Differentiable Dynamics and Bifurcation Theory. Academic Press 1989. J.A. Sanders and F. Verhulst, Averaging Methods in Nonlinear Dynamical Systems. Appl Math Sciences 59, Springer-Verlag 1985.
(219 Ruelle, D., An inequality for the entropy of differentiable maps, Boletim da Sociedade Brasileira Matemática 9(1978), 83-87. [220) Ruelle, D., Elements of differentiable dynamics and bifurcation theory, Acad. Press, 1989.
A self-contained comprehensive introduction to the mathematical theory of dynamical systems for students and researchers in mathematics, science and engineering.
Newhouse , S. E. ( 1980 ) Lectures on Dynamical Systems , Prog . in Math . , 8 , pp . 1-114 , Birkhauser , Boston . ... Ruelle , D. ( 1989 ) Elements of Differentiable Dynamics and Bifurcation Theory , Academic Press .
Several distinctive aspects make Dynamical Systems unique, including: treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas ...
Zbl. 601.58003 Ruelle, D. (1989): Elements of Differentiable Dynamics and Bifurcation Theory. Academic Press, Boston. Zbl. 684.58001 Sharkovskij, A.N., Kolyada, S.F., Sivak, A.G., Fedorenko, V.V. (1989): Dynamics of One-Dimensional ...
Mané R.: Ergodic theory and differentiable dynamics. Springer-Verlag, Berlin, Heidelberg ... May R.M.: Simple mathematical models with very complicated dynamics. ... Ruelle D.: Elements of differentiable dynamics and bifurcation theory.
51 (1973), 136 [Rue2] D. Ruelle: "Elements of differentiable dynamics and bifurcation theory”; Academic Press (London) 1989 [Sat1] D.H. Sattinger: "Topics in stability and bifurcation theory”; Lecture Notes in Mathematics 309, ...