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Chaos [[electronic resource] ] : from simple models to complex systems / / Massimo Cencini, Fabio Cecconi, Angelo Vulpiani
| Chaos [[electronic resource] ] : from simple models to complex systems / / Massimo Cencini, Fabio Cecconi, Angelo Vulpiani |
| Autore | Cencini Massimo |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2010 |
| Descrizione fisica | 1 online resource (482 p.) |
| Disciplina | 515.39 |
| Altri autori (Persone) |
CecconiFabio
VulpianiA |
| Collana | Series on advances in statistical mechanics |
| Soggetto topico |
Chaotic behavior in systems
Dynamics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-75833-0
9786612758331 981-4277-66-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 Derivation of the Lorenz model; 3.3 The Hénon-Heiles system; 3.4 What did we learn and what will we learn?; BoxB. 5 Correlation functions; 3.5 Closing remark; 3.6 Exercises; 4. Probabilistic Approach to Chaos; 4.1 An informal probabilistic approach; 4.2 Time evolution of the probability density; BoxB. 6 Markov Processes; A: Finite states Markov Chains; B: Continuous Markov processes; C: Dynamical systems with additive noise; 4.3 Ergodicity; 4.3.1 An historical interlude on ergodic theory; BoxB. 7 Poincaré recurrence theorem 4.3.2 Abstract formulation of the Ergodic theory 4.4 Mixing; 4.5 Markov chains and chaoticmaps; 4.6 Natural measure; 4.7 Exercises; 5. Characterization of Chaotic Dynamical Systems; 5.1 Strange attractors; 5.2 Fractals and multifractals; 5.2.1 Box counting dimension; 5.2.2 The stretching and folding mechanism; 5.2.3 Multifractals; BoxB. 8 Brief excursion on Large Deviation Theory; 5.2.4 Grassberger-Procaccia algorithm; 5.3 Characteristic Lyapunov exponents; BoxB. 9 Algorithm for computing Lyapunov Spectrum; 5.3.1 Oseledec theorem and the law of large numbers 5.3.2 Remarks on the Lyapunov exponents 5.3.2.1 Lyapunov exponents are topological invariant; 5.3.2.2 Relationship between Lyapunov exponents of flows and Poincaré maps; 5.3.3 Fluctuation statistics of finite time Lyapunov exponents; 5.3.4 Lyapunov dimension; BoxB. 10 Mathematical chaos; A: Hyperbolic sets and Anosov systems; B: SRB measure; C: The Arnold cat map; 5.4 Exercises; 6. From Order to Chaos in Dissipative Systems; 6.1 The scenarios for the transition to turbulence; 6.1.1 Landau-Hopf; BoxB. 11 Hopf bifurcation; BoxB. 12 The Van der Pol oscillator and the averaging technique 6.1.2 Ruelle-Takens |
| Record Nr. | UNINA-9910455859203321 |
Cencini Massimo
|
||
| Hackensack, N.J., : World Scientific, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chaos [[electronic resource] ] : from simple models to complex systems / / Massimo Cencini, Fabio Cecconi, Angelo Vulpiani
| Chaos [[electronic resource] ] : from simple models to complex systems / / Massimo Cencini, Fabio Cecconi, Angelo Vulpiani |
| Autore | Cencini Massimo |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2010 |
| Descrizione fisica | 1 online resource (482 p.) |
| Disciplina | 515.39 |
| Altri autori (Persone) |
CecconiFabio
VulpianiA |
| Collana | Series on advances in statistical mechanics |
| Soggetto topico |
Chaotic behavior in systems
Dynamics |
| ISBN |
1-282-75833-0
9786612758331 981-4277-66-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 Derivation of the Lorenz model; 3.3 The Hénon-Heiles system; 3.4 What did we learn and what will we learn?; BoxB. 5 Correlation functions; 3.5 Closing remark; 3.6 Exercises; 4. Probabilistic Approach to Chaos; 4.1 An informal probabilistic approach; 4.2 Time evolution of the probability density; BoxB. 6 Markov Processes; A: Finite states Markov Chains; B: Continuous Markov processes; C: Dynamical systems with additive noise; 4.3 Ergodicity; 4.3.1 An historical interlude on ergodic theory; BoxB. 7 Poincaré recurrence theorem 4.3.2 Abstract formulation of the Ergodic theory 4.4 Mixing; 4.5 Markov chains and chaoticmaps; 4.6 Natural measure; 4.7 Exercises; 5. Characterization of Chaotic Dynamical Systems; 5.1 Strange attractors; 5.2 Fractals and multifractals; 5.2.1 Box counting dimension; 5.2.2 The stretching and folding mechanism; 5.2.3 Multifractals; BoxB. 8 Brief excursion on Large Deviation Theory; 5.2.4 Grassberger-Procaccia algorithm; 5.3 Characteristic Lyapunov exponents; BoxB. 9 Algorithm for computing Lyapunov Spectrum; 5.3.1 Oseledec theorem and the law of large numbers 5.3.2 Remarks on the Lyapunov exponents 5.3.2.1 Lyapunov exponents are topological invariant; 5.3.2.2 Relationship between Lyapunov exponents of flows and Poincaré maps; 5.3.3 Fluctuation statistics of finite time Lyapunov exponents; 5.3.4 Lyapunov dimension; BoxB. 10 Mathematical chaos; A: Hyperbolic sets and Anosov systems; B: SRB measure; C: The Arnold cat map; 5.4 Exercises; 6. From Order to Chaos in Dissipative Systems; 6.1 The scenarios for the transition to turbulence; 6.1.1 Landau-Hopf; BoxB. 11 Hopf bifurcation; BoxB. 12 The Van der Pol oscillator and the averaging technique 6.1.2 Ruelle-Takens |
| Record Nr. | UNINA-9910780723103321 |
|
Cencini Massimo
|
||
| Hackensack, N.J., : World Scientific, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chaos [[electronic resource] ] : from simple models to complex systems / / Massimo Cencini, Fabio Cecconi, Angelo Vulpiani
| Chaos [[electronic resource] ] : from simple models to complex systems / / Massimo Cencini, Fabio Cecconi, Angelo Vulpiani |
| Autore | Cencini Massimo |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2010 |
| Descrizione fisica | 1 online resource (482 p.) |
| Disciplina | 515.39 |
| Altri autori (Persone) |
CecconiFabio
VulpianiA |
| Collana | Series on advances in statistical mechanics |
| Soggetto topico |
Chaotic behavior in systems
Dynamics |
| ISBN |
1-282-75833-0
9786612758331 981-4277-66-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 Derivation of the Lorenz model; 3.3 The Hénon-Heiles system; 3.4 What did we learn and what will we learn?; BoxB. 5 Correlation functions; 3.5 Closing remark; 3.6 Exercises; 4. Probabilistic Approach to Chaos; 4.1 An informal probabilistic approach; 4.2 Time evolution of the probability density; BoxB. 6 Markov Processes; A: Finite states Markov Chains; B: Continuous Markov processes; C: Dynamical systems with additive noise; 4.3 Ergodicity; 4.3.1 An historical interlude on ergodic theory; BoxB. 7 Poincaré recurrence theorem 4.3.2 Abstract formulation of the Ergodic theory 4.4 Mixing; 4.5 Markov chains and chaoticmaps; 4.6 Natural measure; 4.7 Exercises; 5. Characterization of Chaotic Dynamical Systems; 5.1 Strange attractors; 5.2 Fractals and multifractals; 5.2.1 Box counting dimension; 5.2.2 The stretching and folding mechanism; 5.2.3 Multifractals; BoxB. 8 Brief excursion on Large Deviation Theory; 5.2.4 Grassberger-Procaccia algorithm; 5.3 Characteristic Lyapunov exponents; BoxB. 9 Algorithm for computing Lyapunov Spectrum; 5.3.1 Oseledec theorem and the law of large numbers 5.3.2 Remarks on the Lyapunov exponents 5.3.2.1 Lyapunov exponents are topological invariant; 5.3.2.2 Relationship between Lyapunov exponents of flows and Poincaré maps; 5.3.3 Fluctuation statistics of finite time Lyapunov exponents; 5.3.4 Lyapunov dimension; BoxB. 10 Mathematical chaos; A: Hyperbolic sets and Anosov systems; B: SRB measure; C: The Arnold cat map; 5.4 Exercises; 6. From Order to Chaos in Dissipative Systems; 6.1 The scenarios for the transition to turbulence; 6.1.1 Landau-Hopf; BoxB. 11 Hopf bifurcation; BoxB. 12 The Van der Pol oscillator and the averaging technique 6.1.2 Ruelle-Takens |
| Record Nr. | UNINA-9910816631903321 |
|
Cencini Massimo
|
||
| Hackensack, N.J., : World Scientific, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A random walk in physics : beyond black holes and time-travels / / Massimo Cencini [and three others]
| A random walk in physics : beyond black holes and time-travels / / Massimo Cencini [and three others] |
| Autore | Cencini Massimo |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (220 pages) : illustrations (some color) |
| Disciplina | 530 |
| Soggetto topico | Physics |
| ISBN | 3-030-72531-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chapter 1 Introduction -- Chapter 2 Atoms, Irreversibility, Probability, Statistical Mechanics, Entropy -- Chapter 3 Probability, Entropy, Chaos -- Chapter 4 Chaos, Prediction -- Chapter 5 Prediction, Turbulence, Models -- Chapter 6 Models, Richardson -- Chapter 7 Boltzmann, Statistical Mechanics, Brownian Motion -- Chapter 8 Boltzmann, Atoms, Statistical Mechanics, Mesoscale Systems -- Chapter 9 Prediction: Chaos, Poincaré, Richardson, Models, Big data -- Chapter 10 Statistical Mechanics: Atoms, Boltzmann, Maxwell. |
| Record Nr. | UNISA-996466846703316 |
|
Cencini Massimo
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
A random walk in physics : beyond black holes and time-travels / / Massimo Cencini [and three others]
| A random walk in physics : beyond black holes and time-travels / / Massimo Cencini [and three others] |
| Autore | Cencini Massimo |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (220 pages) : illustrations (some color) |
| Disciplina | 530 |
| Soggetto topico | Physics |
| ISBN | 3-030-72531-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chapter 1 Introduction -- Chapter 2 Atoms, Irreversibility, Probability, Statistical Mechanics, Entropy -- Chapter 3 Probability, Entropy, Chaos -- Chapter 4 Chaos, Prediction -- Chapter 5 Prediction, Turbulence, Models -- Chapter 6 Models, Richardson -- Chapter 7 Boltzmann, Statistical Mechanics, Brownian Motion -- Chapter 8 Boltzmann, Atoms, Statistical Mechanics, Mesoscale Systems -- Chapter 9 Prediction: Chaos, Poincaré, Richardson, Models, Big data -- Chapter 10 Statistical Mechanics: Atoms, Boltzmann, Maxwell. |
| Record Nr. | UNINA-9910485587403321 |
|
Cencini Massimo
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||