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Dynamical system and chaosan introduction with applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dynamical system and chaosby Rui Dilão.
Reminder of title:	an introduction with applications /
Author:	Dilão, Rui.
Published:	Cham :Springer International Publishing :2023.
Description:	ix, 326 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	System theory.
Online resource:	https://doi.org/10.1007/978-3-031-25154-2
ISBN:	9783031251542$q(electronic bk.)

Dynamical system and chaosan introduction with applications /
Dilão, Rui.

Dynamical system and chaosan introduction with applications /[electronic resource] :by Rui Dilão. - Cham :Springer International Publishing :2023. - ix, 326 p. :ill., digital ;24 cm. - UNITEXT for physics,2198-7890. - UNITEXT for physics..

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.

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.

ISBN: 9783031251542$q(electronic bk.)

Standard No.: 10.1007/978-3-031-25154-2doiSubjects--Topical Terms:

183989
System theory.

LC Class. No.: Q295 / .D55 2023

Dewey Class. No.: 003

Dynamical system and chaosan introduction with applications /
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245 1 0 $a Dynamical system and chaos $h [electronic resource] : $b an introduction with applications / $c by Rui Dilão.
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505 0 $a 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.
520 $a 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.
650 0 $a System theory. $3 183989
650 0 $a Dynamics. $3 189568
650 0 $a Chaotic behavior in systems. $3 182904
650 1 4 $a Complex Systems. $3 558544
650 2 4 $a Dynamical Systems. $3 913342
650 2 4 $a Mathematical Methods in Physics. $3 273796
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773 0 $t Springer Nature eBook
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856 4 0 $u https://doi.org/10.1007/978-3-031-25154-2
950 $a Physics and Astronomy (SpringerNature-11651)