Download e-book for iPad: A First Course in Dynamics: with a Panorama of Recent by Boris Hasselblatt,Anatole Katok

By Boris Hasselblatt,Anatole Katok

the idea of dynamical structures is an important mathematical self-discipline heavily intertwined with all major components of arithmetic. It has significantly motivated examine in lots of sciences and given upward push to the tremendous new quarter variously referred to as utilized dynamics, nonlinear technological know-how, or chaos conception. This advent for senior undergraduate and starting graduate scholars of arithmetic, physics, and engineering combines mathematical rigor with copious examples of significant functions. It covers the vital topological and probabilistic notions in dynamics starting from Newtonian mechanics to coding concept. Readers needn't be acquainted with manifolds or degree idea; the one prerequisite is a simple undergraduate research path. The authors commence through describing the wide selection of clinical and mathematical questions that dynamics can handle. They then use a development of examples to offer the ideas and instruments for describing asymptotic habit in dynamical platforms, steadily expanding the extent of complexity. the ultimate chapters introduce smooth advancements and purposes of dynamics. topics comprise contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, unusual attractors, twist maps, and KAM-theory.

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A First Course in Dynamics: with a Panorama of Recent Developments by Boris Hasselblatt,Anatole Katok

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