Chaos [[electronic resource]]

• Record Nr.: UNISA996394540903316
• Pubbl/distr/stampa: [London, : printed for Livewel Chapman, at the Crown in Popes-head-Alley, 1659]
• Descrizione fisica: 8 p
• Soggetti: Toleration; Great Britain History Commonwealth and Protectorate, 1649-1660 Early works to 1800; Great Britain Politics and government 1649-1660 Early works to 1800
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Caption title.; Imprint from colophon.; Annotation on Thomason copy: "1659 June. 28".; Reproduction of the original in the British Library.
• Nota di contenuto: Intro -- INTRODUCTION -- CONTENTS -- 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(1 - x) -- 1.7 Sensitive Dependence on Initial Conditions -- 1.8 Itineraries -- CHALLENGE 1: 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 &amp -- #969 -- -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 [equation omitted] 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 -- APPENDIX A MATRIX ALGEBRA -- A.1 Eigenvalues and Eigenvectors -- A.2 Coordinate Changes -- A.3 Matrix Times Circle Equals Ellipse -- APPENDIX 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 -- BIBLIOGRAPHY -- INDEX.
• Sommario/riassunto: eebo-0018