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1.

図書

図書
Tadeusz Iwaniec and Gaven Martin
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 2001  xv, 552 p. ; 25 cm
シリーズ名: Oxford mathematical monographs
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2.

図書

図書
Patricia Melin and Oscar Castillo
出版情報: London : Taylor & Francis, 2002  xi, 249 p. ; 26 cm.
シリーズ名: Numerical insights / series editor, A. Sydow ; v. 2
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3.

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
4.

図書

図書
edited by Y.B. Fu, R.W. Ogden
出版情報: Cambridge ; New York : Cambridge University Press, 2001  xi, 525 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 283
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Preface
Elements of the theory of finite elasticity / R. W. Ogden1:
Hyperelastic Bell materials: retrospection, experiment, theory / M. F. Beatty2:
Universal results in finite elasticity / G. Saccomandi3:
Equilibrium solutions for compressible nonlinearly elastic materials / C. O. Horgan4:
Exact integrals and solutions for finite deformations of the incompressible Varga elastic materials / J. M. Hill5:
Shear / Ph. Boulanger ; M. Hayes6:
Elastic membranes / D. M. Haughton7:
Elements of the theory of elastic surfaces / D. J. Steigmann8:
Singularity theory and nonlinear bifurcation analysis / Y.-C. Chen9:
Perturbation methods and nonlinear stability analysis / Y. B. Fu10:
Nonlinear dispersive waves in a circular rod composed of a Mooney-Rivlin material / H.-H. Dai11:
Strain-energy functions with multiple local minima: modeling phase transformations using finite thermo-elasticity / R. Abeyaratne ; K. Bhattacharya ; J. K. Knowles12:
Pseudo-elasticity and stress softening / 13:
Preface
Elements of the theory of finite elasticity / R. W. Ogden1:
Hyperelastic Bell materials: retrospection, experiment, theory / M. F. Beatty2:
5.

図書

図書
Stuart S. Antman
出版情報: New York : Springer, c2005  xviii, 831 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 107
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6.

図書

図書
Vassili N. Kolokoltsov
出版情報: Cambridge, UK ; Tokyo : Cambridge University Press, 2010  xvii, 375 p. ; 23 cm
シリーズ名: Cambridge tracts in mathematics ; 182
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Preface
Basic definitions, notation and abbreviations
Introduction / 1:
Nonlinear Markov chains / 1.1:
Examples: replicator dynamics, the Lotka-Volterra equations, epidemics, coagulation / 1.2:
Interacting-particle approximation for discrete mass-exchange processes / 1.3:
Nonlinear Lévy processes and semigroups / 1.4:
Multiple coagulation, fragmentation and collisions; extended Smoluchovski and Boltzmann models / 1.5:
Replicator dynamics of evolutionary game theory / 1.6:
Interacting Markov processes; mean field and kth-order interactions / 1.7:
Classical kinetic equations of statistical mechanics: Vlasov, Boltzmann, Landau / 1.8:
Moment measures, correlation functions and the propagation of chaos / 1.9:
Nonlinear Markov processes and semigroups; nonlinear martingale problems / 1.10:
Tools from Markov process theory / Part I:
Probability and analysis / 2:
Semigroups, propagators and generators / 2.1:
Feller processes and conditionally positive operators / 2.2:
Jump-type Markov processes / 2.3:
Connection with evolution equations / 2.4:
Probabilistic constructions / 3:
Stochastic integrals and SDEs driven by nonlinear Lévy noise / 3.1:
Nonlinear version of Ito's approach to SDEs / 3.2:
Homogeneous driving noise / 3.3:
An alternative approximation scheme / 3.4:
Regularity of solutions / 3.5:
Coupling of Lévy processes / 3.6:
Analytical constructions / 4:
Comparing analytical and probabilistic tools / 4.1:
Integral generators: one-barrier case / 4.2:
Integral generators: two-barrier case / 4.3:
Generators of order at most one: well-posedness / 4.4:
Generators of order at most one: regularity / 4.5:
Further techniques: martingale problem, Sobolev spaces, heat kernels etc. / 4.6:
Unbounded coefficients / 5:
A growth estimate for Feller processes / 5.1:
Extending Feller processes / 5.2:
Invariant domains / 5.3:
Nonlinear Markov processes and semigroups / Part II:
Integral generators / 6:
Overview / 6.1:
Bounded generators / 6.2:
Additive bounds for rates: existence / 6.3:
Additive bounds for rates: well-posedness / 6.4:
A tool for proving uniqueness / 6.5:
Multiplicative bounds for rates / 6.6:
Another existence result / 6.7:
Conditional positivity / 6.8:
Generators of Lévy-Khintchine type / 7:
Variable coefficients via fixed-point arguments / 7.1:
Nonlinear SDE construction / 7.3:
Smoothness with respect to initial data / 7.4:
Motivation and plan; a warm-up result / 8.1:
Lévy-Khintchine-type generators / 8.2:
Jump-type models / 8.3:
Estimates for Smoluchovski's equation / 8.4:
Propagation and production of moments for the Boltzmann equation / 8.5:
Estimates for the Boltzmann equation / 8.6:
Applications to interacting particles / Part III:
The dynamic law of large numbers / 9:
Manipulations with generators / 9.1:
Interacting diffusions, stable-like and Vlasov processes / 9.2:
Pure jump models: probabilistic approach / 9.3:
Rates of convergence for Smoluchovski coagulation / 9.4:
Rates of convergence for Boltzmann collisions / 9.5:
The dynamic central limit theorem / 10:
Generators for fluctuation processes / 10.1:
Weak CLT with error rates: the Smoluchovski and Boltzmann models, mean field limits and evolutionary games / 10.2:
Summarizing the strategy followed / 10.3:
Infinite-dimensional Ornstein-Uhlenbeck processes / 10.4:
Full CLT for coagulation processes (a sketch) / 10.5:
Developments and comments / 11:
Measure-valued processes as stochastic dynamic LLNs for interacting particles; duality of one-dimensional processes / 11.1:
Discrete nonlinear Markov games and controlled processes; the modeling of deception / 11.2:
Nonlinear quantum dynamic semigroups and the nonlinear Schrödinger equation / 11.3:
Curvilinear Ornstein-Uhlenbeck processes (linear and nonlinear) and stochastic geodesic flows on manifolds / 11.4:
The structure of generators / 11.5:
Bibliographical comments / 11.6:
Appendices
Distances on measures / A:
Topology on càdlàg paths / B:
Convergence of processes in Skorohod spaces / C:
Vector-valued ODEs / D:
Pseudo-differential operator notation / E:
Variational derivatives / F:
Geometry of collisions / G:
A combinatorial lemma / H:
Approximation of infinite-dimensional functions / I:
Bogolyubov chains, generating functionals and Fock-space calculus / J:
Infinite-dimensional Riccati equations / K:
References
Index
Preface
Basic definitions, notation and abbreviations
Introduction / 1:
7.

図書

図書
Julius S. Bendat
出版情報: New York : Wiley, c1998  xiii, 474 p. ; 24 cm
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Linear Systems, Random Data
Zero-Memory Nonlinear Systems
Direct and Reverse MI/SO
Techniques for Analysis and Identification of Nonlinear Systems
Parallel Linear and Nonlinear Systems
Determination of Physical Parameters with Memory in Nonlinear Systems
Nonlinear System Response Properties of a Naval Frigate from Measured Ocean Engineering Data
Nonlinear System Response Properties of a Naval Barge from Measured Ocean Engineering Data
Bilinear and Trilinear Systems
Input Output Relations for Bilinear and Trilinear Systems
References
Index
Glossary of Symbols
Linear Systems, Random Data
Zero-Memory Nonlinear Systems
Direct and Reverse MI/SO
8.

図書

図書
J. Bourgain
出版情報: Providence, RI : American Mathematical Society, c1999  viii, 182 p. ; 26 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 46
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Introduction and summary
An overview of results on the Cauchy problem for NLS
Further comments 3D $H^1$-critical defocusing NLS Global wellposedness below energy norm
Nonlinear Schrodinger equation with periodic boundary conditions
Growth of Sobolev norms in linear
Schrodinger equations with smooth time dependent potential
Zakharov systems
References
Index
Introduction and summary
An overview of results on the Cauchy problem for NLS
Further comments 3D $H^1$-critical defocusing NLS Global wellposedness below energy norm
9.

図書

図書
I.I. Vorovich ; English edition edited by L.P. Lebedev ; translated by Michael Grinfeld
出版情報: New York : Springer, c1999  xvi, 388 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 133
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10.

図書

図書
Thierry Aubin
出版情報: Berlin : Springer-Verlag, 1998  xvii, 395 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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