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Record Nr. |
UNINA9910816631903321 |
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Autore |
Cencini Massimo |
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Titolo |
Chaos : from simple models to complex systems / / Massimo Cencini, Fabio Cecconi, Angelo Vulpiani |
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Pubbl/distr/stampa |
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Hackensack, N.J., : World Scientific, c2010 |
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ISBN |
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1-282-75833-0 |
9786612758331 |
981-4277-66-5 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (482 p.) |
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Collana |
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Series on advances in statistical mechanics ; ; v. 17 |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Chaotic behavior in systems |
Dynamics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Contents; Preface; Introduction; Historical note; Overview of the book; Hints on how to use/read this book; Introduction to Dynamical Systems and Chaos; 1. First Encounter with Chaos; 1.1 Prologue; 1.2 The nonlinear pendulum; 1.3 The damped nonlinear pendulum; 1.4 The vertically driven and damped nonlinear pendulum; 1.5 What about the predictability of pendulum evolution?; 1.6 Epilogue; 2. The Language of Dynamical Systems; 2.1 Ordinary Differential Equations (ODE); 2.1.1 Conservative and dissipative dynamical systems; BoxB. 1 Hamiltonian dynamics |
A: Symplectic structure and Canonical Transformations B: Integrable systems and Action-Angle variables; 2.1.2 PoincaréMap; 2.2 Discrete time dynamical systems: maps; 2.2.1 Two dimensional maps; 2.2.1.1 The Hénon Map; 2.2.1.2 Two-dimensional symplectic maps; 2.3 The role of dimension; 2.4 Stability theory; 2.4.1 Classification of fixed points and linear stability analysis; BoxB. 2 A remark on the linear stability of symplectic maps; 2.4.2 Nonlinear stability; 2.4.2.1 Limit cycles; 2.4.2.2 Lyapunov Theorem; 2.5 Exercises; 3. Examples of Chaotic Behaviors; 3.1 The logisticmap |
BoxB. 3 Topological conjugacy 3.2 The Lorenzmodel; BoxB. 4 |
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