Dynamical system and chaos : an introduction with applications / Rui Dilão.
Dilão, Rui, author.
2023
Q295 .D55 2023
Available Online

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Title Dynamical system and chaos : an introduction with applications / Rui Dilão.
Author Dilão, Rui, author.
ISBN 9783031251542 electronic book
3031251547 electronic book
9783031251535
3031251539
DOI https://doi.org/10.1007/978-3-031-25154-2
Published Cham, Switzerland : Springer, [2023]
Language English
Description 1 online resource (ix, 326 pages) : illustrations.
Other Standard Identifiers 10.1007/978-3-031-25154-2 doi
Call Number Q295 .D55 2023
Dewey Decimal Classification 003
Summary This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems. Some freedom is used in the more formal aspects, using only proofs when there is an algorithmic advantage or because a result is simple and powerful. The first part is an introductory course on dynamical systems theory. It can be taught at the master's level during one semester, not requiring specialized mathematical training. In the second part, the author describes some applications of the theory of dynamical systems. Topics often appear in modern dynamical systems and complexity theories, such as singular perturbation theory, delayed equations, cellular automata, fractal sets, maps of the complex plane, and stochastic iterations of function systems are briefly explored for advanced students. The author also explores applications in mechanics, electromagnetism, celestial mechanics, nonlinear control theory, and macroeconomy. A set of problems consolidating the knowledge of the different subjects, including more elaborated exercises, are provided for all chapters.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on online resource; title from digital title page (viewed on May 25, 2023).
Series UNITEXT for physics.
Available in Other Form DYNAMICAL SYSTEM AND CHAOS.
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All Resources
Differential Equations as Dynamical Systems
Stability of fixed points
Difference equations as dynamical systems
Classification of fixed points
Hamiltonian systems
Numerical Methods.-Strange Attractors and Maps of an Interval
Stable, Unstable and Centre manifolds.-Dynamics in the Centre Manifold
Lyapunov Exponents and Oseledets Theorem
Chaos
Limit and Recurrent Sets.-Poincare Maps
The Poincare-Bendixon Theorem
Bifurcations of Differential Equations.-Singular Pertubations and Ducks.-Strange Attractors in Delay Equations
Complexity of Strange Attractors.-Intermittency
Cellular Automata
Maps of the Complex Plane
Stochastic Iteration of Function Systems
Linear Maps on the Torus and Symbolic Dynamics
Parametric Resonance
Robot Motion
Synchronisation of Pendula
Synchronisation of Clocks
Chaos in Stormer Problem.-Introduction to Celestial mechanics
Introduction to non-Liner control Theory
Appendices.

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