The Resource Nonlinear Dynamics and Chaotic Phenomena : an Introduction, Bhimsen K. Shivamoggi

Nonlinear Dynamics and Chaotic Phenomena : an Introduction, Bhimsen K. Shivamoggi

Label
Nonlinear Dynamics and Chaotic Phenomena : an Introduction
Title
Nonlinear Dynamics and Chaotic Phenomena
Title remainder
an Introduction
Statement of responsibility
Bhimsen K. Shivamoggi
Creator
Author
Author
Subject
Genre
Language
eng
Summary
"This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics--integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker's transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-de Vries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence--a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special emphasis on some aspects of fluid dynamics and plasma physics reflecting the author's involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on. This book has grown out of the author's lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum. This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering. This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises."--Publisher's description
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Shivamoggi, Bhimsen K
Dewey number
003.857
Illustrations
illustrations
Index
index present
LC call number
Q172.5.C45
LC item number
S48 2014
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Fluid mechanics and its applications
Series volume
Volume 103
http://library.link/vocab/subjectName
  • Chaotic behavior in systems
  • Nonlinear theories
  • Dynamics
  • SCIENCE
  • TECHNOLOGY & ENGINEERING
  • Physique
  • Astronomie
  • Chaotic behavior in systems
  • Dynamics
  • Nonlinear theories
  • Engineering
  • Mechanical Engineering
  • Vibration, Dynamical Systems, Control
  • Engineering Fluid Dynamics
Label
Nonlinear Dynamics and Chaotic Phenomena : an Introduction, Bhimsen K. Shivamoggi
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-94-007-7094-2
Instantiates
Publication
Copyright
Note
Previous edition: Dordrecht; London: Kluwer Academic, 1997
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1.1.
  • First-Order Systems.
  • 1.1.1.
  • Dynamical System.
  • 1.1.2.
  • Lipschitz Condition.
  • 1.1.3.
  • Gronwall's Lemma.
  • 1.1.4.
  • Linear Equations.
  • Introduction to Chaotic Behavior in Nonlinear Dynamics.
  • 1.1.5.
  • Autonomous Systems.
  • 1.1.6.
  • Stability of Equilibrium Points.
  • 1.1.6.1.
  • Liapunov and Asymptotic Stability.
  • 1.1.6.2.
  • Liapunov Function Method.
  • 1.1.7.
  • Center Manifold Theorem.
  • Phase-Space Dynamics.
  • 1.2.
  • Phase-Plane Analysis.
  • 1.3.
  • Fully Nonlinear Evolution.
  • 1.4.
  • Non-autonomous Systems
  • Conservative Dynamical Systems.
  • Dissipative Dynamical Systems.
  • Routes to Chaos.
  • Turbulence in Fluids
  • 1.
  • Nonlinear Ordinary Differential Equations.
  • 2.4.
  • Break-up of Bifurcations Under Perturbations.
  • 2.5.
  • Bifurcation Theory for One-Dimensional Maps.
  • Appendix.
  • The Normal Form Reduction
  • 2.
  • Bifurcation Theory.
  • 2.1.
  • Stability and Bifurcation.
  • 2.2.
  • Saddle-Node, Transcritical and Pitchfork Bifurcations.
  • 2.3.
  • Hopf Bifurcation.
  • 3.4.
  • The Hamilton-Jacobi Equation.
  • 3.5.
  • Action-Angle Variables.
  • 3.6.
  • Infinitesimal Canonical Transformations.
  • 3.7.
  • Poisson's Brackets
  • 3.
  • Hamiltonian Dynamics.
  • 3.1.
  • Hamilton's Equations.
  • 3.2.
  • Phase Space.
  • 3.3.
  • Canonical Transformations.
  • 4.4.
  • Canonical Perturbation Theory.
  • 4.5.
  • Kolmogorov-Arnol'd-Moser Theory.
  • 4.6.
  • Breakdown of Integrability and Criteria for Transition to Chaos.
  • 4.6.1.
  • Local Criteria.
  • 4.6.2.
  • Local Stability vs. Global Stability.
  • 4.
  • 4.6.3.
  • Global Criteria.
  • 4.7.
  • Magnetic Island Overlap and Stochasticity in Magnetic Confinement Systems.
  • Appendix.
  • The Problem of Internal Resonances in Nonlinearly-Coupled Systems
  • Integrable Systems.
  • 4.1.
  • Separable Hamiltonian Systems.
  • 4.2.
  • Integrable Systems.
  • 4.3.
  • Dynamics on the Tori.
  • 5.4.
  • Twist Maps.
  • 5.5.
  • Tangent Maps.
  • 5.6.
  • Poincaré-Birkhoff Fixed-Point Theorem.
  • 5.7.
  • Homoclinic and Heteroclinic Points.
  • 5.8.
  • Quantitative Measures of Chaos.
  • 5.
  • 5.8.1.
  • Liapunov Exponents.
  • 5.8.2.
  • Kolmogorov Entropy.
  • 5.8.3.
  • Autocorrelation Function.
  • 5.8.4.
  • Power Spectra.
  • 5.9.
  • Ergodicity and Mixing.
  • Chaos in Conservative Systems.
  • 5.9.1.
  • Ergodicity.
  • 5.9.2.
  • Mixing.
  • 5.9.3.
  • Baker's Transformation.
  • 5.9.4.
  • Lagrangian Chaos in Fluids
  • 5.1.
  • Phase-Space Dynamics of Conservative Systems.
  • 5.2.
  • Poincaré's Surface of Section.
  • 5.3.
  • Area-Preserving Mappings.
  • 6.3.1.
  • Examples of Fractals.
  • 6.3.2.
  • Box-Counting Method.
  • 6.4.
  • Multi-fractals.
  • 6.5.
  • Analysis of Time-Series Data.
  • 6.6.
  • The Lorenz Attractor.
  • 6.
  • 6.6.1.
  • Equilibrium Solutions and Their Stability.
  • 6.6.2.
  • Slightly Supercritical Case.
  • 6.6.3.
  • Existence of an Attractor.
  • 6.6.4.
  • Chaotic Behavior of the Nonlinear Solutions.
  • 6.7.
  • Period-Doubling Bifurcations.
  • Chaos in Dissipative Systems.
  • 6.7.1.
  • Difference Equations.
  • 6.7.2.
  • The Logistic Map.
  • Appendix A.
  • The Hausdorff-Besicovitch Dimension.
  • Appendix B.
  • The Derivation of Lorenz's Equation.
  • Appendix C.
  • The Derivation of Universality for One-Dimensional Maps
  • 6.1.
  • Phase-Space Dynamics of Dissipative Systems.
  • 6.2.
  • Strange Attractors.
  • 6.3.
  • Fractals.
  • 7.4.
  • Shallow Water Waves.
  • 7.5.
  • Ion-Acoustic Waves.
  • 7.6.
  • Basic Properties of the Korteweg-de Vries Equation.
  • 7.6.1.
  • Effect of Nonlinearity.
  • 7.6.2.
  • Effect of Dispersion.
  • 7.
  • 7.6.3.
  • Similarity Transformation.
  • 7.6.4.
  • Stokes Waves: Periodic Solutions.
  • 7.6.5.
  • Solitary Waves.
  • 7.6.6.
  • Periodic Cnoidal Wave Solutions.
  • 7.6.7.
  • Interacting Solitary Waves: Hirota's Method.
  • Solitons.
  • 7.7.
  • Inverse-Scattering Transform Method.
  • 7.7.1.
  • Time Evolution of the Scattering Data.
  • 7.7.2.
  • Inverse Scattering Problem: Gel'fand-Levitan-Marchenko Equation.
  • 7.7.3.
  • Direct-Scattering Problem.
  • 7.7.4.
  • Inverse-Scattering Problem.
  • 7.1.
  • 7.8.
  • Conservation Laws.
  • 7.9.
  • Lax Formulation.
  • 7.10.
  • Bäcklund Transformations
  • Fermi-Pasta-Ulam Recurrence.
  • 7.2.
  • Korteweg-de Vries Equation.
  • 7.3.
  • Waves in an Anharmonic Lattice.
  • 8.
  • Singularity Analysis and the Painlevé Property of Dynamical Systems.
  • 8.1.
  • The Painlevé Property.
  • 8.2.
  • Singularity Analysis.
  • 8.3.
  • The Painlevé Property for Partial Differential Equations
Dimensions
unknown
Edition
Second edition.
Extent
1 online resource (xxvii, 375 pages)
File format
unknown
Form of item
online
Isbn
9789400770942
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-94-007-7094-2
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)880386031
  • (OCoLC)ocn880386031
Label
Nonlinear Dynamics and Chaotic Phenomena : an Introduction, Bhimsen K. Shivamoggi
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-94-007-7094-2
Publication
Copyright
Note
Previous edition: Dordrecht; London: Kluwer Academic, 1997
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1.1.
  • First-Order Systems.
  • 1.1.1.
  • Dynamical System.
  • 1.1.2.
  • Lipschitz Condition.
  • 1.1.3.
  • Gronwall's Lemma.
  • 1.1.4.
  • Linear Equations.
  • Introduction to Chaotic Behavior in Nonlinear Dynamics.
  • 1.1.5.
  • Autonomous Systems.
  • 1.1.6.
  • Stability of Equilibrium Points.
  • 1.1.6.1.
  • Liapunov and Asymptotic Stability.
  • 1.1.6.2.
  • Liapunov Function Method.
  • 1.1.7.
  • Center Manifold Theorem.
  • Phase-Space Dynamics.
  • 1.2.
  • Phase-Plane Analysis.
  • 1.3.
  • Fully Nonlinear Evolution.
  • 1.4.
  • Non-autonomous Systems
  • Conservative Dynamical Systems.
  • Dissipative Dynamical Systems.
  • Routes to Chaos.
  • Turbulence in Fluids
  • 1.
  • Nonlinear Ordinary Differential Equations.
  • 2.4.
  • Break-up of Bifurcations Under Perturbations.
  • 2.5.
  • Bifurcation Theory for One-Dimensional Maps.
  • Appendix.
  • The Normal Form Reduction
  • 2.
  • Bifurcation Theory.
  • 2.1.
  • Stability and Bifurcation.
  • 2.2.
  • Saddle-Node, Transcritical and Pitchfork Bifurcations.
  • 2.3.
  • Hopf Bifurcation.
  • 3.4.
  • The Hamilton-Jacobi Equation.
  • 3.5.
  • Action-Angle Variables.
  • 3.6.
  • Infinitesimal Canonical Transformations.
  • 3.7.
  • Poisson's Brackets
  • 3.
  • Hamiltonian Dynamics.
  • 3.1.
  • Hamilton's Equations.
  • 3.2.
  • Phase Space.
  • 3.3.
  • Canonical Transformations.
  • 4.4.
  • Canonical Perturbation Theory.
  • 4.5.
  • Kolmogorov-Arnol'd-Moser Theory.
  • 4.6.
  • Breakdown of Integrability and Criteria for Transition to Chaos.
  • 4.6.1.
  • Local Criteria.
  • 4.6.2.
  • Local Stability vs. Global Stability.
  • 4.
  • 4.6.3.
  • Global Criteria.
  • 4.7.
  • Magnetic Island Overlap and Stochasticity in Magnetic Confinement Systems.
  • Appendix.
  • The Problem of Internal Resonances in Nonlinearly-Coupled Systems
  • Integrable Systems.
  • 4.1.
  • Separable Hamiltonian Systems.
  • 4.2.
  • Integrable Systems.
  • 4.3.
  • Dynamics on the Tori.
  • 5.4.
  • Twist Maps.
  • 5.5.
  • Tangent Maps.
  • 5.6.
  • Poincaré-Birkhoff Fixed-Point Theorem.
  • 5.7.
  • Homoclinic and Heteroclinic Points.
  • 5.8.
  • Quantitative Measures of Chaos.
  • 5.
  • 5.8.1.
  • Liapunov Exponents.
  • 5.8.2.
  • Kolmogorov Entropy.
  • 5.8.3.
  • Autocorrelation Function.
  • 5.8.4.
  • Power Spectra.
  • 5.9.
  • Ergodicity and Mixing.
  • Chaos in Conservative Systems.
  • 5.9.1.
  • Ergodicity.
  • 5.9.2.
  • Mixing.
  • 5.9.3.
  • Baker's Transformation.
  • 5.9.4.
  • Lagrangian Chaos in Fluids
  • 5.1.
  • Phase-Space Dynamics of Conservative Systems.
  • 5.2.
  • Poincaré's Surface of Section.
  • 5.3.
  • Area-Preserving Mappings.
  • 6.3.1.
  • Examples of Fractals.
  • 6.3.2.
  • Box-Counting Method.
  • 6.4.
  • Multi-fractals.
  • 6.5.
  • Analysis of Time-Series Data.
  • 6.6.
  • The Lorenz Attractor.
  • 6.
  • 6.6.1.
  • Equilibrium Solutions and Their Stability.
  • 6.6.2.
  • Slightly Supercritical Case.
  • 6.6.3.
  • Existence of an Attractor.
  • 6.6.4.
  • Chaotic Behavior of the Nonlinear Solutions.
  • 6.7.
  • Period-Doubling Bifurcations.
  • Chaos in Dissipative Systems.
  • 6.7.1.
  • Difference Equations.
  • 6.7.2.
  • The Logistic Map.
  • Appendix A.
  • The Hausdorff-Besicovitch Dimension.
  • Appendix B.
  • The Derivation of Lorenz's Equation.
  • Appendix C.
  • The Derivation of Universality for One-Dimensional Maps
  • 6.1.
  • Phase-Space Dynamics of Dissipative Systems.
  • 6.2.
  • Strange Attractors.
  • 6.3.
  • Fractals.
  • 7.4.
  • Shallow Water Waves.
  • 7.5.
  • Ion-Acoustic Waves.
  • 7.6.
  • Basic Properties of the Korteweg-de Vries Equation.
  • 7.6.1.
  • Effect of Nonlinearity.
  • 7.6.2.
  • Effect of Dispersion.
  • 7.
  • 7.6.3.
  • Similarity Transformation.
  • 7.6.4.
  • Stokes Waves: Periodic Solutions.
  • 7.6.5.
  • Solitary Waves.
  • 7.6.6.
  • Periodic Cnoidal Wave Solutions.
  • 7.6.7.
  • Interacting Solitary Waves: Hirota's Method.
  • Solitons.
  • 7.7.
  • Inverse-Scattering Transform Method.
  • 7.7.1.
  • Time Evolution of the Scattering Data.
  • 7.7.2.
  • Inverse Scattering Problem: Gel'fand-Levitan-Marchenko Equation.
  • 7.7.3.
  • Direct-Scattering Problem.
  • 7.7.4.
  • Inverse-Scattering Problem.
  • 7.1.
  • 7.8.
  • Conservation Laws.
  • 7.9.
  • Lax Formulation.
  • 7.10.
  • Bäcklund Transformations
  • Fermi-Pasta-Ulam Recurrence.
  • 7.2.
  • Korteweg-de Vries Equation.
  • 7.3.
  • Waves in an Anharmonic Lattice.
  • 8.
  • Singularity Analysis and the Painlevé Property of Dynamical Systems.
  • 8.1.
  • The Painlevé Property.
  • 8.2.
  • Singularity Analysis.
  • 8.3.
  • The Painlevé Property for Partial Differential Equations
Dimensions
unknown
Edition
Second edition.
Extent
1 online resource (xxvii, 375 pages)
File format
unknown
Form of item
online
Isbn
9789400770942
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-94-007-7094-2
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)880386031
  • (OCoLC)ocn880386031

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