An introduction to dynamical systems

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An introduction to dynamical systems / D.K. Arrowsmith, C.M. Place

資料種別:

図書

出版情報:

Cambridge [England] ; New York : Cambridge University Press, 1990

形態:

423 p. ; 26 cm

著者名:

ISBN:

9780521303620 [0521303621] (: hard)
9780521316507 [0521316502] (: pbk)

書誌ID:

BA10593081

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Bibliography: p. [413]-416
Includes index

主題:

Differentiable dynamical systems

言語:

英語

目次情報:

Preface

Diffeomorphisms and flows / 1：

Introduction / 1.1：

Elementary dynamics of diffeomorphisms / 1.2：

Definitions / 1.2.1：

Diffeomorphisms of the circle / 1.2.2：

Flows and differential equations / 1.3：

Invariant sets / 1.4：

Conjugacy / 1.5：

Equivalence of flows / 1.6：

Poincare maps and suspensions / 1.7：

Periodic non-autonomous systems / 1.8：

Hamiltonian flows and Poincare maps / 1.9：

Exercises

Local properties of flows and diffeomorphisms / 2：

Hyperbolic linear diffeomorphisms and flows / 2.1：

Hyperbolic non-linear fixed points / 2.2：

Diffeomorphisms / 2.2.1：

Flows / 2.2.2：

Normal forms for vector fields / 2.3：

Non-hyperbolic singular points of vector fields / 2.4：

Normal forms for diffeomorphisms / 2.5：

Time-dependent normal forms / 2.6：

Centre manifolds / 2.7：

Blowing-up techniques on R[superscript 2] / 2.8：

Polar blowing-up / 2.8.1：

Directional blowing-up / 2.8.2：

Structural stability, hyperbolicity and homoclinic points / 3：

Structural stability of linear systems / 3.1：

Local structural stability / 3.2：

Flows on two-dimensional manifolds / 3.3：

Anosov diffeomorphisms / 3.4：

Horseshoe diffeomorphisms / 3.5：

The canonical example / 3.5.1：

Dynamics on symbol sequences / 3.5.2：

Symbolic dynamics for the horseshoe diffeomorphism / 3.5.3：

Hyperbolic structure and basic sets / 3.6：

Homoclinic points / 3.7：

The Melnikov function / 3.8：

Local bifurcations I: planar vector fields and diffeomorphisms on R / 4：

Saddle-node and Hopf bifurcations / 4.1：

Saddle-node bifurcation / 4.2.1：

Hopf bifurcation / 4.2.2：

Cusp and generalised Hopf bifurcations / 4.3：

Cusp bifurcation / 4.3.1：

Generalised Hopf bifurcations / 4.3.2：

Diffeomorphisms on R / 4.4：

D[subscript x]f(0) = +1: the fold bifurcation / 4.4.1：

D[subscript x]f(0) = -1: the flip bifurcation / 4.4.2：

The logistic map / 4.5：

Local bifurcations II: diffeomorphisms on R[superscript 2] / 5：

Arnold's circle map / 5.1：

Irrational rotations / 5.3：

Rational rotations and weak resonance / 5.4：

Vector field approximations / 5.5：

Irrational [beta] / 5.5.1：

Rational [beta] = p/q, q [greater than or equal] 3 / 5.5.2：

Rational [beta] = p/q, q = 1, 2 / 5.5.3：

Equivariant versal unfoldings for vector field approximations / 5.6：

q = 2 / 5.6.1：

q = 3 / 5.6.2：

q = 4 / 5.6.3：

q [greater than or equal] 5 / 5.6.4：

Unfoldings of rotations and shears / 5.7：

Area-preserving maps and their perturbations / 6：

Rational rotation numbers and Birkhoff periodic points / 6.1：

The Poincare-Birkhoff Theorem / 6.2.1：

Vector field approximations and island chains / 6.2.2：

Irrational rotation numbers and the KAM Theorem / 6.3：

The Aubry-Mather Theorem / 6.4：

Invariant Cantor sets for homeomorphisms on S[superscript 1] / 6.4.1：

Twist homeomorphisms and Mather sets / 6.4.2：

Generic elliptic points / 6.5：

Weakly dissipative systems and Birkhoff attractors / 6.6：

Birkhoff periodic orbits and Hopf bifurcations / 6.7：

Double invariant circle bifurcations in planar maps / 6.8：

Hints for exercises

References

Index

Preface

Diffeomorphisms and flows / 1：

Introduction / 1.1：

Elementary dynamics of diffeomorphisms / 1.2：

Definitions / 1.2.1：

Diffeomorphisms of the circle / 1.2.2：

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