Clark Robinson

Dynamical Systems (eBook, PDF)

Stability, Symbolic Dynamics, and Chaos

• Format: PDF

Produktbeschreibung

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 through examples and at a level accessible to a beginning graduate student; focusing on multidimensional systems of real variables. The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects. What's New in the Second Edition?: A revised discussion of the saddle node bifurcation; a new section on the horseshoe for a flow with a transverse homoclinic point; material on horseshoes for nontransverse homoclinic points, indicating recent extensions to the understanding of how horseshoes arise; information proving the ergodicity of a hyperbolic toral automorphism; a new chapter on Hamiltonian systems. TOC:Introduction.- One Dimensional Dynamics by Iteration.- Chaos and Its Measurement.- Linear Systems.- Analysis Near Fixed Points and Periodic Orbits.- Hamiltonian Systems.- Bifurcation of Periodic Points.- Examples of Hyperbolic Sets and Attractors.- Measurement of Chaos in Higher Dimensions.- Global Theory of Hyperbolic Systems.- Generic Properties.- Smoothness of Stable Manifolds and Applications.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 520
• Erscheinungstermin: 17. November 1998
• Englisch
• ISBN-13: 9781482227871
• Artikelnr.: 57589392

Autorenporträt

Clark Robinson

Inhaltsangabe

IntroductionOne Dimensional Dynamics by IterationChaos and Its MeasurementLinear SystemsAnalysis near Fixed Points and Periodic OrbitsHamiltonian SystemsBifurcation of Periodic PointsExamples of Hyperbolic Sets and AttractorsMeasurement of Chaos in Higher DimensionsGlobal Theory of Hyperbolic SystemsGeneric PropertiesSmoothness of Stable Manifolds and Applications

Rezensionen

"...was impressed with the teachability of this text and with the exercises at the end of each chapter, which seemed be nicely graded in difficulty."
-D. Givoli, APPLIED MECHANICS REVIEWS