東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Dynamical system and chaos = an intr...

Dilão, Rui.

Linked to FindBook

Google Book

Amazon

博客來

Dynamical system and chaos = an introduction with applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dynamical system and chaos/ by 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.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	System theory. -
Online resource:	https://doi.org/10.1007/978-3-031-25154-2
ISBN:	9783031251542

Dynamical system and chaos = an 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

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

525574
System theory.

LC Class. No.: Q295 / .D55 2023

Dewey Class. No.: 003

Dynamical system and chaos = an introduction with applications /
LDR:03295nmm a2200337 a 4500 001 2318021
003 DE-He213
005 20230406163230.0
006 m d
007 cr nn 008maaau
008 230902s2023 sz s 0 eng d
020 $a 9783031251542 $q (electronic bk.)
020 $a 9783031251535 $q (paper)
024 7 $a 10.1007/978-3-031-25154-2 $2 doi
035 $a 978-3-031-25154-2
040 $a GP $c GP
041 0 $a eng
050 4 $a Q295 $b .D55 2023
072 7 $a GPFC $2 bicssc
072 7 $a SCI055000 $2 bisacsh
072 7 $a GPFC $2 thema
082 0 4 $a 003 $2 23
090 $a Q295 $b .D576 2023
100 1 $a Dilão, Rui. $3 3632663
245 1 0 $a Dynamical system and chaos $h [electronic resource] : $b an introduction with applications / $c by Rui Dilão.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a ix, 326 p. : $b ill., digital ; $c 24 cm.
490 1 $a UNITEXT for physics, $x 2198-7890
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 525574
650 0 $a Dynamics. $3 519830
650 0 $a Chaotic behavior in systems. $3 524350
650 1 4 $a Complex Systems. $3 1566441
650 2 4 $a Dynamical Systems. $3 3538746
650 2 4 $a Mathematical Methods in Physics. $3 890898
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a UNITEXT for physics. $3 2068732
856 4 0 $u https://doi.org/10.1007/978-3-031-25154-2
950 $a Physics and Astronomy (SpringerNature-11651)