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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
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In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.Abstract:
Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors.- Global Bifurcations.- Local Codimension Two Bifurcations of Flows.- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index.read more
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e-approximation of differential inclusions
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Symmetries within chaos: A route to effective mixing
TL;DR: In this paper, the authors show that simple two-dimensional time-periodic flows can produce chaotic mixing, where the mixing is not always complete; depending on the choice of the period, there can exist large dynamic structures, called islands, that stretch and compress in a timeperiodic manner but remain segregated even after long times.