Chaos - nieuw boek

EAN (ISBN-13): 9783540780366
ISBN (ISBN-10): 354078036X
pocket book
Verschijningsjaar: 1997
Uitgever: Springer

Boek bevindt zich in het datenbestand sinds 2016-05-21T15:50:12+02:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2021-08-26T11:51:54+02:00 (Amsterdam)
ISBN/EAN: 354078036X

ISBN - alternatieve schrijfwijzen:
3-540-78036-X, 978-3-540-78036-6
alternatieve schrijfwijzen en verwante zoekwoorden:
Auteur van het boek: alligood, alligo, sauer
Titel van het boek: chaos introduction dynamical systems

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Gegevens van de uitgever

Auteur: Kathleen Alligood; Tim Sauer; J.A. Yorke
Titel: Textbooks in Mathematical Sciences; Chaos - An Introduction to Dynamical Systems
Uitgeverij: Springer; Springer Berlin
603 Bladzijden
Verschijningsjaar: 1997-05-01
Berlin; Heidelberg; DE
Gewicht: 0,985 kg
Taal: Engels
85,55 € (DE)
87,95 € (AT)
106,60 CHF (CH)
Not available, publisher indicates OP

BC; Book; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; integration; hamiltonian system; approximation; Eigenvalue; system; calculus; fixed-point theorem; behavior; time; manifold; bifurcation; stability; derivative; eigenvector; differential equation; C; Analysis; Mathematics and Statistics; Complex Systems; Statistical Physics and Dynamical Systems; Statistische Physik; Dynamik und Statik; Statistische Physik; EA

1 One-Dimensional Maps.- 1.1 One-Dimensional Maps.- 1.2 Cobweb Plot: Graphical Representation of an Orbit.- 1.3 Stability of Fixed Points.- 1.4 Periodic Points.- 1.5 The Family of Logistic Maps.- 1.6 The Logistic Map G(x) = 4x(l ? x).- 1.7 Sensitive Dependence on Initial Conditions.- 1.8 Itineraries.- Challenge l: Period Three Implies Chaos.- Exercises.- Lab Visit 1: Boom, Bust, and Chaos in the Beetle Census.- 2 Two-Dimensional Maps.- 2.1 Mathematical Models.- 2.2 Sinks, Sources, and Saddles.- 2.3 Linear Maps.- 2.4 Coordinate Changes.- 2.5 Nonlinear Maps and the Jacobian Matrix.- 2.6 Stable and Unstable Manifolds.- 2.7 Matrix Times Circle Equals Ellipse.- Challenge 2: Counting the Periodic Orbits of Linear Maps on a Torus.- Exercises.- Lab Visit 2: Is the Solar System Stable?.- 3 Chaos.- 3.1 Lyapunov Exponents.- 3.2 Chaotic Orbits.- 3.3 Conjugacy and the Logistic Map.- 3.4 Transition Graphs and Fixed Points.- 3.5 Basins of Attraction.- Challenge 3: Sharkovskii’s Theorem.- Exercises.- Lab Visit 3: Periodicity and Chaos in a Chemical Reaction.- 4 Fractals.- 4.1 Cantor Sets.- 4.2 Probabilistic Constructions of Fractals.- 4.3 Fractals from Deterministic Systems.- 4.4 Fractal Basin Boundaries.- 4.5 Fractal Dimension.- 4.6 Computing the Box-Counting Dimension.- 4.7 Correlation Dimension.- Challenge 4: Fractal Basin Boundaries and the Uncertainty Exponent.- Exercises.- Lab Visit 4: Fractal Dimension in Experiments.- 5 Chaos in Two-Dimensional Maps.- 5.1 Lyapunov Exponents.- 5.2 Numerical Calculation of Lyapunov Exponents.- 5.3 Lyapunov Dimension.- 5.4 A Two-Dimensional Fixed-Point Theorem.- 5.5 Markov Partitions.- 5.6 The Horseshoe Map.- Challenge 5: Computer Calculations and Shadowing.- Exercises.- Lab Visit 5: Chaos in Simple Mechanical Devices.- 6 Chaotic Attractors.- 6.1 Forward Limit Sets.- 6.2 Chaotic Attractors.- 6.3 Chaotic Attractors of Expanding Interval Maps.- 6.4 Measure.- 6.5 Natural Measure.- 6.6 Invariant Measure for One-Dimensional Maps.- Challenge 6: Invariant Measure for the Logistic Map.- Exercises.- Lab Visit 6: Fractal Scum.- 7 Differential Equations.- 7.1 One-Dimensional Linear Differential Equations.- 7.2 One-Dimensional Nonlinear Differential Equations.- 7.3 Linear Differential Equations in More than One Dimension.- 7.4 Nonlinear Systems.- 7.5 Motion in a Potential Field.- 7.6 Lyapunov Functions.- 7.7 Lotka-Volterra Models.- Challenge 7: A Limit Cycle in the van der Pol System.- Exercises.- Lab Visit 7: Fly vs. Fly.- 8 Periodic Orbits and Limit Sets.- 8.1 Limit Sets for Planar Differential Equations.- 8.2 Properties of ?-Limit Sets.- 8.3 Proof of the Poincaré-Bendixson Theorem.- Challenge 8: Two Incommensurate Frequencies Form a Torus.- Exercises.- Lab Visit 8: Steady States and Periodicity in a Squid Neuron.- 9 Chaos in Differential Equations.- 9.1 The Lorenz Attractor.- 9.2 Stability in the Large, Instability in the Small.- 9.3 The Rössler Attractor.- 9.4 Chua’s Circuit.- 9.5 Forced Oscillators.- 9.6 Lyapunov Exponents in Flows.- Challenge 9: Synchronization of Chaotic Orbits.- Exercises.- Lab Visit 9: Lasers in Synchronization.- 10 Stable Manifolds and Crises.- 10.1 The Stable Manifold Theorem.- 10.2 Homoclinic and Heteroclinic Points.- 10.3 Crises.- 10.4 Proof of the Stable Manifold Theorem.- 10.5 Stable and Unstable Manifolds for Higher Dimensional Maps.- Challenge 10: The Lakes of Wada.- Exercises.- Lab Visit 10: The Leaky Faucet: Minor Irritation or Crisis?.- 11 Bifurcations.- 11.1 Saddle-Node and Period-Doubling Bifurcations.- 11.2 Bifurcation Diagrams.- 11.3 Continuability.- 11.4 Bifurcations of One-Dimensional Maps.- 11.5 Bifurcations in Plane Maps: Area-Contracting Case.- 11.6 Bifurcations in Plane Maps: Area-Preserving Case.- 11.7 Bifurcations in Differential Equations.- 11.8 Hopf Bifurcations.- Challenge 11: Hamiltonian Systems and the Lyapunov Center Theorem.- Exercises.- Lab Visit 11: Iron + Sulfuric Acid ? Hopf Bifurcation.- 12 Cascades.- 12.1 Cascades and 4.669201609.- 12.2 Schematic Bifurcation Diagrams.- 12.3 Generic Bifurcations.- 12.4 The Cascade Theorem.- Challenge 12: Universality in Bifurcation Diagrams.- Exercises.- Lab Visit 12: Experimental Cascades.- 13 State Reconstruction from Data.- 13.1 Delay Plots from Time Series.- 13.2 Delay Coordinates.- 13.3 Embedology.- Challenge 13: Box-Counting Dimension and Intersection.- A Matrix Algebra.- A.1 Eigenvalues and Eigenvectors.- A.2 Coordinate Changes.- A.3 Matrix Times Circle Equals Ellipse.- B Computer Solution of Odes.- B.1 ODE Solvers.- B.2 Error in Numerical Integration.- B.3 Adaptive Step-Size Methods.- Answers and Hints to Selected Exercises.