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1.

図書

図書
J.M.T. Thompson and H.B. Stewart
出版情報: Chichester [West Sussex] : Wiley, c2002  xxii, 437 p. ; 23 cm
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Preface
Preface to the First Edition
Acknowledgements from the First Edition
Introduction / 1:
Historical background / 1.1:
Chaotic dynamics in Duffing's oscillator / 1.2:
Attractors and bifurcations / 1.3:
Basic Concepts of Nonlinear Dynamics / Part I:
An overview of nonlinear phenomena / 2:
Undamped, unforced linear oscillator / 2.1:
Undamped, unforced nonlinear oscillator / 2.2:
Damped, unforced linear oscillator / 2.3:
Damped, unforced nonlinear oscillator / 2.4:
Forced linear oscillator / 2.5:
Forced nonlinear oscillator: periodic attractors / 2.6:
Forced nonlinear oscillator: chaotic attractor / 2.7:
Point attractors in autonomous systems / 3:
The linear oscillator / 3.1:
Nonlinear pendulum oscillations / 3.2:
Evolving ecological systems / 3.3:
Competing point attractors / 3.4:
Attractors of a spinning satellite / 3.5:
Limit cycles in autonomous systems / 4:
The single attractor / 4.1:
Limit cycle in a neural system / 4.2:
Bifurcations of a chemical oscillator / 4.3:
Multiple limit cycles in aeroelastic galloping / 4.4:
Topology of two-dimensional phase space / 4.5:
Periodic attractors in driven oscillators / 5:
The Poincare map / 5.1:
Linear resonance / 5.2:
Nonlinear resonance / 5.3:
The smoothed variational equation / 5.4:
Variational equation for subharmonics / 5.5:
Basins of attraction by mapping techniques / 5.6:
Resonance of a self-exciting system / 5.7:
The ABC of nonlinear dynamics / 5.8:
Chaotic attractors in forced oscillators / 6:
Relaxation oscillations and heartbeat / 6.1:
The Birkhoff-Shaw chaotic attractor / 6.2:
Systems with nonlinear restoring force / 6.3:
Stability and bifurcations of equilibria and cycles / 7:
Liapunov stability and structural stability / 7.1:
Centre manifold theorem / 7.2:
Local bifurcations of equilibrium paths / 7.3:
Local bifurcations of cycles / 7.4:
Basin changes at local bifurcations / 7.5:
Prediction of incipient instability / 7.6:
Iterated Maps as Dynamical Systems / Part II:
Stability and bifurcation of maps / 8:
Stability of one-dimensional maps / 8.1:
Bifurcations of one-dimensional maps / 8.3:
Stability of two-dimensional maps / 8.4:
Bifurcations of two-dimensional maps / 8.5:
Basin changes at local bifurcations of limit cycles / 8.6:
Chaotic behaviour of one- and two-dimensional maps / 9:
General outline / 9.1:
Theory for one-dimensional maps / 9.2:
Bifurcations to chaos / 9.3:
Bifurcation diagram of one-dimensional maps / 9.4:
Henon map / 9.5:
Flows, Outstructures, and Chaos / Part III:
The geometry of recurrence / 10:
Finite-dimensional dynamical systems / 10.1:
Types of recurrent behaviour / 10.2:
Hyperbolic stability types for equilibria / 10.3:
Hyperbolic stability types for limit cycles / 10.4:
Implications of hyperbolic structure / 10.5:
The Lorenz system / 11:
A model of thermal convection / 11.1:
First convective instability / 11.2:
The chaotic attractor of Lorenz / 11.3:
Geometry of a transition to chaos / 11.4:
Rossler's band / 12:
The simply folded band in an autonomous system / 12.1:
Return map and bifurcations / 12.2:
Smale's horseshoe map / 12.3:
Transverse homoclinic trajectories / 12.4:
Spatial chaos and localized buckling / 12.5:
Geometry of bifurcations / 13:
Local bifurcations / 13.1:
Global bifurcations in the phase plane / 13.2:
Bifurcations of chaotic attractors / 13.3:
Applications in the Physical Sciences / Part IV:
Subharmonic resonances of an offshore structure / 14:
Basic equation and non-dimensional form / 14.1:
Analytical solution for each domain / 14.2:
Digital computer program / 14.3:
Resonance response curves / 14.4:
Effect of damping / 14.5:
Computed phase projections / 14.6:
Multiple solutions and domains of attraction / 14.7:
Chaotic motions of an impacting system / 15:
Resonance response curve / 15.1:
Application to moored vessels / 15.2:
Period-doubling and chaotic solutions / 15.3:
Escape from a potential well / 16:
Analytical formulation / 16.1:
Overview of the steady-state response / 16.3:
The two-band chaotic attractor / 16.4:
Resonance of the steady states / 16.5:
Transients and basins of attraction / 16.6:
Homoclinic phenomena / 16.7:
Heteroclinic phenomena / 16.8:
Indeterminate bifurcations / 16.9:
Appendix
Illustrated Glossary
Bibliography
Online Resources
Index
Preface
Preface to the First Edition
Acknowledgements from the First Edition
2.

図書

図書
Edward Ott
出版情報: Cambridge [England] ; New York : Cambridge University Press, 1993  xii, 385 p. ; 26 cm
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Preface
Introduction and overview / 1:
One-dimensional maps / 2:
Strange attractors and fractal dimensions / 3:
Dynamical properties of chaotic systems / 4:
Nonattracting chaotic sets / 5:
Quasiperiodicity / 6:
Chaos in Hamiltonian systems / 7:
Chaotic transitions / 8:
Multifractals / 9:
Control and synchronization of chaos / 10:
Quantum chaos / 11:
Preface
Introduction and overview / 1:
One-dimensional maps / 2:
3.

図書

図書
Frank C. Hoppensteadt
出版情報: New York ; Tokyo : Springer-Verlag, c1993  xvii, 305 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 94
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Linear Systems
Dynamical Systems
Stability Methods for Nonlinear Systems
Bifurcation and Topological Methods
Regular Perturbation Methods
Iterations and Perturbations
Methods of Averaging
Quasistatic-State Approximations
References
Index
Linear Systems
Dynamical Systems
Stability Methods for Nonlinear Systems
4.

図書

図書
Robert L. Devaney
出版情報: Redwood City, Calif. ; Tokyo : Addison-Wesley Pub. Co., c1989  xvi, 336 p., [8] p. of col. plates ; 25 cm
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5.

図書

図書
David Ruelle
出版情報: Princeton, N.J. : Princeton University Press, c1991  vii, 195 p. ; 23 cm
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6.

図書

図書
edited by E.R. Pike and L.A. Lugiato
出版情報: Bristol : A. Hilger, c1987  xiii, 249 p. ; 24 cm
シリーズ名: Malvern physics series ; 3
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7.

図書

図書
Robert L. Devaney
出版情報: Redwood City, Calif. ; Wokingham : Addison-Wesley, c1987  xii, 320 p. ; 25 cm
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8.

図書

図書
Stephen Wiggins
出版情報: New York ; Tokyo : Springer-Verlag, c1990  xiv, 672 p. ; 25 cm
シリーズ名: Texts in applied mathematics ; 2
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