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Chaos [[electronic resource]]
| Chaos [[electronic resource]] |
| Pubbl/distr/stampa | [London, : printed for Livewel Chapman, at the Crown in Popes-head-Alley, 1659] |
| Descrizione fisica | 8 p |
| Soggetto topico | Toleration |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 & -- #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. |
| Record Nr. | UNISA-996394540903316 |
| [London, : printed for Livewel Chapman, at the Crown in Popes-head-Alley, 1659] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
A defence against the poyson of Satans designe [[electronic resource] ] : cast out of his mouth by James Nayler, in his pretended answer to An antidote against the spreading infections of the spirit of Antichrist, lately published by Thomas Moor. Shewing how manifestly the said J. N. hath altered the sayings of T. M. in that book, and grossely belyed him, and the truth attested by him, so as every reader may see, in most of the things spoken to, and by that may judge of the rest of his accusations, that might require some farther witnesse than J. N. or T. M. to prove, or disprove them. With some discovery of the emptiness and unsoundness of his pretended answers, with his altering the sayings, and corrupting the sense of the scriptures therein. Likewise of the wolf appearing under the sheepskin, in the beginning, and close of his book. By Thomas Moor, Junior
| A defence against the poyson of Satans designe [[electronic resource] ] : cast out of his mouth by James Nayler, in his pretended answer to An antidote against the spreading infections of the spirit of Antichrist, lately published by Thomas Moor. Shewing how manifestly the said J. N. hath altered the sayings of T. M. in that book, and grossely belyed him, and the truth attested by him, so as every reader may see, in most of the things spoken to, and by that may judge of the rest of his accusations, that might require some farther witnesse than J. N. or T. M. to prove, or disprove them. With some discovery of the emptiness and unsoundness of his pretended answers, with his altering the sayings, and corrupting the sense of the scriptures therein. Likewise of the wolf appearing under the sheepskin, in the beginning, and close of his book. By Thomas Moor, Junior |
| Autore | Moore Thomas, Junior |
| Pubbl/distr/stampa | London, : printed for Livewel Chapman, at the Crown in Popes-head-Alley, 1656 |
| Descrizione fisica | [2], 71, [1] p |
| Altri autori (Persone) | NaylorJames <1617?-1660.> |
| Soggetto topico |
Society of Friends
Quakers - England |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996394645503316 |
Moore Thomas, Junior
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| London, : printed for Livewel Chapman, at the Crown in Popes-head-Alley, 1656 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
