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

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

Label
An introduction to dynamical systems
Title
An introduction to dynamical systems
Statement of responsibility
D.K. Arrowsmith, C.M. Place
Creator
Contributor
Subject
Genre
Language
eng
Cataloging source
DLC
http://library.link/vocab/creatorName
Arrowsmith, D. K
Index
index present
LC call number
QA614.8
LC item number
.A77 1990
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Place, C. M
http://library.link/vocab/subjectName
  • Differentiable dynamical systems
  • Differentiaalsystemen
  • Differentieerbaarheid
  • Dynamische systemen
  • Systèmes dynamiques différentiables
  • Dynamique différentiable
  • Differentiable dynamical systems
  • Dynamische systemen
  • Differentiaalsystemen
  • Differentieerbaarheid
  • Dynamique différentiable
  • Differenzierbares dynamisches System
Label
An introduction to dynamical systems, D.K. Arrowsmith, C.M. Place
Instantiates
Publication
Note
Includes index
Bibliography note
Includes bibliographical references
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1.2.2.
  • 5.
  • Local bifurcations II: diffeomorphisms on R[superscript 2]
  • 5.1.
  • Introduction
  • 5.2.
  • Arnold's circle map
  • 5.3.
  • Irrational rotations
  • 5.4.
  • Rational rotations and weak resonance
  • Diffeomorphisms of the circle
  • 5.5.
  • Vector field approximations
  • 5.5.1.
  • Irrational [beta]
  • 5.5.2.
  • Rational [beta] = p/q, q [greater than or equal] 3
  • 5.5.3.
  • Rational [beta] = p/q, q = 1, 2
  • 5.6.
  • Equivariant versal unfoldings for vector field approximations
  • 1.3.
  • 5.6.1.
  • q = 2
  • 5.6.2.
  • q = 3
  • 5.6.3.
  • q = 4
  • 5.6.4.
  • q [greater than or equal] 5
  • 5.7.
  • Unfoldings of rotations and shears
  • Flows and differential equations
  • 6.
  • Area-preserving maps and their perturbations
  • 6.1.
  • Introduction
  • 6.2.
  • Rational rotation numbers and Birkhoff periodic points
  • 6.2.1.
  • The Poincare-Birkhoff Theorem
  • 6.2.2.
  • Vector field approximations and island chains
  • 1.4.
  • 6.3.
  • Irrational rotation numbers and the KAM Theorem
  • 6.4.
  • The Aubry-Mather Theorem
  • 6.4.1.
  • Invariant Cantor sets for homeomorphisms on S[superscript 1]
  • 6.4.2.
  • Twist homeomorphisms and Mather sets
  • 6.5.
  • Generic elliptic points
  • Invariant sets
  • 6.6.
  • Weakly dissipative systems and Birkhoff attractors
  • 6.7.
  • Birkhoff periodic orbits and Hopf bifurcations
  • 6.8.
  • Double invariant circle bifurcations in planar maps
  • 1.5.
  • Conjugacy
  • 1.6.
  • Equivalence of flows
  • 1.
  • 1.7.
  • Poincare maps and suspensions
  • 1.8.
  • Periodic non-autonomous systems
  • 1.9.
  • Hamiltonian flows and Poincare maps
  • 2.
  • Local properties of flows and diffeomorphisms
  • 2.1.
  • Hyperbolic linear diffeomorphisms and flows
  • Diffeomorphisms and flows
  • 2.2.
  • Hyperbolic non-linear fixed points
  • 2.2.1.
  • Diffeomorphisms
  • 2.2.2.
  • Flows
  • 2.3.
  • Normal forms for vector fields
  • 2.4.
  • Non-hyperbolic singular points of vector fields
  • 1.1.
  • 2.5.
  • Normal forms for diffeomorphisms
  • 2.6.
  • Time-dependent normal forms
  • 2.7.
  • Centre manifolds
  • 2.8.
  • Blowing-up techniques on R[superscript 2]
  • 2.8.1.
  • Polar blowing-up
  • Introduction
  • 2.8.2.
  • Directional blowing-up
  • 3.
  • Structural stability, hyperbolicity and homoclinic points
  • 3.1.
  • Structural stability of linear systems
  • 3.2.
  • Local structural stability
  • 3.3.
  • Flows on two-dimensional manifolds
  • 1.2.
  • 3.4.
  • Anosov diffeomorphisms
  • 3.5.
  • Horseshoe diffeomorphisms
  • 3.5.1.
  • The canonical example
  • 3.5.2.
  • Dynamics on symbol sequences
  • 3.5.3.
  • Symbolic dynamics for the horseshoe diffeomorphism
  • Elementary dynamics of diffeomorphisms
  • 3.6.
  • Hyperbolic structure and basic sets
  • 3.7.
  • Homoclinic points
  • 3.8.
  • The Melnikov function
  • 4.
  • Local bifurcations I: planar vector fields and diffeomorphisms on R
  • 4.1.
  • Introduction
  • 1.2.1.
  • 4.2.
  • Saddle-node and Hopf bifurcations
  • 4.2.1.
  • Saddle-node bifurcation
  • 4.2.2.
  • Hopf bifurcation
  • 4.3.
  • Cusp and generalised Hopf bifurcations
  • 4.3.1.
  • Cusp bifurcation
  • Definitions
  • 4.3.2.
  • Generalised Hopf bifurcations
  • 4.4.
  • Diffeomorphisms on R
  • 4.4.1.
  • D[subscript x]f(0) = +1: the fold bifurcation
  • 4.4.2.
  • D[subscript x]f(0) = -1: the flip bifurcation
  • 4.5.
  • The logistic map
Dimensions
26 cm
Extent
423 pages
Isbn
9780521316507
Isbn Type
(pbk.)
Lccn
89007191
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)19553114
  • (OCoLC)ocm19553114
Label
An introduction to dynamical systems, D.K. Arrowsmith, C.M. Place
Publication
Note
Includes index
Bibliography note
Includes bibliographical references
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 1.2.2.
  • 5.
  • Local bifurcations II: diffeomorphisms on R[superscript 2]
  • 5.1.
  • Introduction
  • 5.2.
  • Arnold's circle map
  • 5.3.
  • Irrational rotations
  • 5.4.
  • Rational rotations and weak resonance
  • Diffeomorphisms of the circle
  • 5.5.
  • Vector field approximations
  • 5.5.1.
  • Irrational [beta]
  • 5.5.2.
  • Rational [beta] = p/q, q [greater than or equal] 3
  • 5.5.3.
  • Rational [beta] = p/q, q = 1, 2
  • 5.6.
  • Equivariant versal unfoldings for vector field approximations
  • 1.3.
  • 5.6.1.
  • q = 2
  • 5.6.2.
  • q = 3
  • 5.6.3.
  • q = 4
  • 5.6.4.
  • q [greater than or equal] 5
  • 5.7.
  • Unfoldings of rotations and shears
  • Flows and differential equations
  • 6.
  • Area-preserving maps and their perturbations
  • 6.1.
  • Introduction
  • 6.2.
  • Rational rotation numbers and Birkhoff periodic points
  • 6.2.1.
  • The Poincare-Birkhoff Theorem
  • 6.2.2.
  • Vector field approximations and island chains
  • 1.4.
  • 6.3.
  • Irrational rotation numbers and the KAM Theorem
  • 6.4.
  • The Aubry-Mather Theorem
  • 6.4.1.
  • Invariant Cantor sets for homeomorphisms on S[superscript 1]
  • 6.4.2.
  • Twist homeomorphisms and Mather sets
  • 6.5.
  • Generic elliptic points
  • Invariant sets
  • 6.6.
  • Weakly dissipative systems and Birkhoff attractors
  • 6.7.
  • Birkhoff periodic orbits and Hopf bifurcations
  • 6.8.
  • Double invariant circle bifurcations in planar maps
  • 1.5.
  • Conjugacy
  • 1.6.
  • Equivalence of flows
  • 1.
  • 1.7.
  • Poincare maps and suspensions
  • 1.8.
  • Periodic non-autonomous systems
  • 1.9.
  • Hamiltonian flows and Poincare maps
  • 2.
  • Local properties of flows and diffeomorphisms
  • 2.1.
  • Hyperbolic linear diffeomorphisms and flows
  • Diffeomorphisms and flows
  • 2.2.
  • Hyperbolic non-linear fixed points
  • 2.2.1.
  • Diffeomorphisms
  • 2.2.2.
  • Flows
  • 2.3.
  • Normal forms for vector fields
  • 2.4.
  • Non-hyperbolic singular points of vector fields
  • 1.1.
  • 2.5.
  • Normal forms for diffeomorphisms
  • 2.6.
  • Time-dependent normal forms
  • 2.7.
  • Centre manifolds
  • 2.8.
  • Blowing-up techniques on R[superscript 2]
  • 2.8.1.
  • Polar blowing-up
  • Introduction
  • 2.8.2.
  • Directional blowing-up
  • 3.
  • Structural stability, hyperbolicity and homoclinic points
  • 3.1.
  • Structural stability of linear systems
  • 3.2.
  • Local structural stability
  • 3.3.
  • Flows on two-dimensional manifolds
  • 1.2.
  • 3.4.
  • Anosov diffeomorphisms
  • 3.5.
  • Horseshoe diffeomorphisms
  • 3.5.1.
  • The canonical example
  • 3.5.2.
  • Dynamics on symbol sequences
  • 3.5.3.
  • Symbolic dynamics for the horseshoe diffeomorphism
  • Elementary dynamics of diffeomorphisms
  • 3.6.
  • Hyperbolic structure and basic sets
  • 3.7.
  • Homoclinic points
  • 3.8.
  • The Melnikov function
  • 4.
  • Local bifurcations I: planar vector fields and diffeomorphisms on R
  • 4.1.
  • Introduction
  • 1.2.1.
  • 4.2.
  • Saddle-node and Hopf bifurcations
  • 4.2.1.
  • Saddle-node bifurcation
  • 4.2.2.
  • Hopf bifurcation
  • 4.3.
  • Cusp and generalised Hopf bifurcations
  • 4.3.1.
  • Cusp bifurcation
  • Definitions
  • 4.3.2.
  • Generalised Hopf bifurcations
  • 4.4.
  • Diffeomorphisms on R
  • 4.4.1.
  • D[subscript x]f(0) = +1: the fold bifurcation
  • 4.4.2.
  • D[subscript x]f(0) = -1: the flip bifurcation
  • 4.5.
  • The logistic map
Dimensions
26 cm
Extent
423 pages
Isbn
9780521316507
Isbn Type
(pbk.)
Lccn
89007191
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)19553114
  • (OCoLC)ocm19553114

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