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Nonlinear Dynamics : A Primer.

By: Contributor(s): Publisher: Cambridge : Cambridge University Press, 2001Copyright date: ©2001Description: 1 online resource (316 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511154737
Subject(s): Genre/Form: Additional physical formats: Print version:: Nonlinear Dynamics : A PrimerDDC classification:
  • 330.0151
LOC classification:
  • QA614.8 .M428 2001
Online resources:
Contents:
Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Statics and dynamics: some elementary concepts -- 1.1 A static problem -- 1.2 A discrete-time dynamic problem -- 1.3 A continuous-time dynamic problem -- 1.4 Flows and maps -- Exercises -- 2 Review of linear systems -- 2.1 Introduction -- 2.2 General solutions of linear systems in continuous time -- 2.3 Continuous systems in the plane -- 2.4 General solutions of linear systems in discrete time -- 2.5 Discrete systems in the plane -- 2.6 An economic example -- Appendix: phase diagrams -- Exercises -- 3 Stability of fixed points -- 3.1 Some formal definitions of stability -- 3.2 The linear approximation -- 3.3 The second or direct method of Lyapunov -- Appendix A: general economic equilibrium -- Appendix B: optimal economic growth -- Appendix C: manifolds and tangent spaces -- Exercises -- 4 Invariant and attracting sets, periodic and quasiperiodic orbits -- 4.1 Invariant and limit sets -- 4.2 Stability and attractiveness of general sets -- 4.3 Attracting sets and attractors -- 4.4 Periodic orbits and their stability -- 4.4.1 Periodic orbits of continuous-time systems -- 4.4.2 Periodic orbits of maps -- 4.5 Quasiperiodic orbits -- Appendix: conservative and dissipative systems -- Exercises -- 5 Local bifurcations -- 5.1 Introduction -- 5.2 Centre manifold theory -- 5.3 Local bifurcations for flows -- 5.3.1 Saddle-node or fold bifurcation -- 5.3.2 Transcritical bifurcation -- 5.3.3 Pitchfork bifurcation -- 5.3.4 Generic bifurcations -- 5.3.5 Hopf bifurcation for flows -- 5.4 Local bifurcations for maps -- 5.4.1 Fold, transcritical and pitchfork bifurcations -- 5.4.2 Flip bifurcation -- 5.4.3 Neimark-Sacker bifurcation -- 5.5 Bifurcations in two-dimensional maps -- Exercises -- 6 Chaotic sets and chaotic attractors -- 6.1 Basic definitions.
6.2 Symbolic dynamics and the shift map -- 6.3 Logistic map with… -- 6.4 Smale horseshoe -- 6.5 Tent map and logistic map -- 6.6 Doubling maps -- 6.7 Chaotic attractors -- 6.8 The Lorenz model -- Exercises -- 7 Characteristic exponents, fractals, homoclinic orbits -- 7.1 Lyapunov characteristic exponents -- 7.2 Fractal dimension -- 7.3 Horseshoes and homoclinic orbits -- 7.3.1 Homoclinic orbits for maps -- 7.3.2 Homoclinic points for flows -- 7.3.3 Horseshoes in the Hénon map -- Exercises -- 8 Transition to chaos -- 8.1 Period-doubling route to chaos -- 8.1.1 Maps of the interval -- 8.1.2 Period 3 -- 8.1.3 The logistic map -- 8.2 Intermittency -- 8.3 Crises -- 8.4 Quasiperiodicity and chaos -- Exercises -- 9 The ergodic approach -- 9.1 Ergodic measures -- 9.1.1 Some elementary measure theory -- 9.1.2 Invariant, ergodic measures -- 9.2 Lyapunov characteristic exponents revisited -- 9.3 Natural, absolutely continuous, SBR measures -- 9.4 Attractors as invariant measures -- 9.5 Predictability, entropy -- 9.6 Isomorphism -- 9.7 Aperiodic and chaotic dynamics -- 9.7.1 Quasiperiodic dynamics -- 9.7.2 Chaotic dynamics -- 9.8 Mixing -- Appendix: Shannon's entropy and Khinchin's axioms -- Exercises -- 10 Deterministic systems and stochastic processes -- 10.1 Bernoulli dynamics -- 10.2 Markov shifts -- 10.3 alpha-congruence -- Further reading -- DIFFERENTAL AND DIFFERENCE EQUATIONS -- STABILITY -- DYNAMICAL SYSTEMS, BIFURCATIONS AND CHAOS -- ERGODIC THEORY -- DYNAMICAL SYSTEM THEORY AND ECONOMICS -- Bibliography -- Subject index.
Summary: An advanced undergraduate and graduate textbook on the theory of nonlinear dynamical systems.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan Available EBKAF000303
Ebrary Ebrary Algeria Available
Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
Ebrary Ebrary Libya Available
Ebrary Ebrary Morocco Available
Ebrary Ebrary Nepal Available EBKNP000303
Ebrary Ebrary Sudan Available
Ebrary Ebrary Tunisia Available
Total holds: 0

Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Statics and dynamics: some elementary concepts -- 1.1 A static problem -- 1.2 A discrete-time dynamic problem -- 1.3 A continuous-time dynamic problem -- 1.4 Flows and maps -- Exercises -- 2 Review of linear systems -- 2.1 Introduction -- 2.2 General solutions of linear systems in continuous time -- 2.3 Continuous systems in the plane -- 2.4 General solutions of linear systems in discrete time -- 2.5 Discrete systems in the plane -- 2.6 An economic example -- Appendix: phase diagrams -- Exercises -- 3 Stability of fixed points -- 3.1 Some formal definitions of stability -- 3.2 The linear approximation -- 3.3 The second or direct method of Lyapunov -- Appendix A: general economic equilibrium -- Appendix B: optimal economic growth -- Appendix C: manifolds and tangent spaces -- Exercises -- 4 Invariant and attracting sets, periodic and quasiperiodic orbits -- 4.1 Invariant and limit sets -- 4.2 Stability and attractiveness of general sets -- 4.3 Attracting sets and attractors -- 4.4 Periodic orbits and their stability -- 4.4.1 Periodic orbits of continuous-time systems -- 4.4.2 Periodic orbits of maps -- 4.5 Quasiperiodic orbits -- Appendix: conservative and dissipative systems -- Exercises -- 5 Local bifurcations -- 5.1 Introduction -- 5.2 Centre manifold theory -- 5.3 Local bifurcations for flows -- 5.3.1 Saddle-node or fold bifurcation -- 5.3.2 Transcritical bifurcation -- 5.3.3 Pitchfork bifurcation -- 5.3.4 Generic bifurcations -- 5.3.5 Hopf bifurcation for flows -- 5.4 Local bifurcations for maps -- 5.4.1 Fold, transcritical and pitchfork bifurcations -- 5.4.2 Flip bifurcation -- 5.4.3 Neimark-Sacker bifurcation -- 5.5 Bifurcations in two-dimensional maps -- Exercises -- 6 Chaotic sets and chaotic attractors -- 6.1 Basic definitions.

6.2 Symbolic dynamics and the shift map -- 6.3 Logistic map with… -- 6.4 Smale horseshoe -- 6.5 Tent map and logistic map -- 6.6 Doubling maps -- 6.7 Chaotic attractors -- 6.8 The Lorenz model -- Exercises -- 7 Characteristic exponents, fractals, homoclinic orbits -- 7.1 Lyapunov characteristic exponents -- 7.2 Fractal dimension -- 7.3 Horseshoes and homoclinic orbits -- 7.3.1 Homoclinic orbits for maps -- 7.3.2 Homoclinic points for flows -- 7.3.3 Horseshoes in the Hénon map -- Exercises -- 8 Transition to chaos -- 8.1 Period-doubling route to chaos -- 8.1.1 Maps of the interval -- 8.1.2 Period 3 -- 8.1.3 The logistic map -- 8.2 Intermittency -- 8.3 Crises -- 8.4 Quasiperiodicity and chaos -- Exercises -- 9 The ergodic approach -- 9.1 Ergodic measures -- 9.1.1 Some elementary measure theory -- 9.1.2 Invariant, ergodic measures -- 9.2 Lyapunov characteristic exponents revisited -- 9.3 Natural, absolutely continuous, SBR measures -- 9.4 Attractors as invariant measures -- 9.5 Predictability, entropy -- 9.6 Isomorphism -- 9.7 Aperiodic and chaotic dynamics -- 9.7.1 Quasiperiodic dynamics -- 9.7.2 Chaotic dynamics -- 9.8 Mixing -- Appendix: Shannon's entropy and Khinchin's axioms -- Exercises -- 10 Deterministic systems and stochastic processes -- 10.1 Bernoulli dynamics -- 10.2 Markov shifts -- 10.3 alpha-congruence -- Further reading -- DIFFERENTAL AND DIFFERENCE EQUATIONS -- STABILITY -- DYNAMICAL SYSTEMS, BIFURCATIONS AND CHAOS -- ERGODIC THEORY -- DYNAMICAL SYSTEM THEORY AND ECONOMICS -- Bibliography -- Subject index.

An advanced undergraduate and graduate textbook on the theory of nonlinear dynamical systems.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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