Chaos: An Introduction to Dynamical SystemsSpringer Science & Business Media, 27 de set. de 2000 - 603 páginas Chaos: An Introduction to Dynamical Systems, was developed and class-tested by a distinguished team of authors at two universities through their teaching of courses based on the material. Intended for courses in nonlinear dynamics offered either in Mathematics or Physics, the text requires only calculus, differential equations, and linear algebra as prerequisites. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits, short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed to be used with any software package. And each chapter ends with a Challenge, which provides students a tour through an advanced topic in the form of an extended exercise. |
Conteúdo
TWODIMENSIONAL MAPS | 43 |
CHAOS | 105 |
FRACTALS | 149 |
CHAOS IN TWODIMENSIONAL MAPS | 193 |
CHAOTIC ATTRACTORS | 231 |
DIFFERENTIAL EQUATIONS | 273 |
PERIODIC ORBITS AND LIMIT SETS | 329 |
CHAOS IN DIFFERENTIAL EQUATIONS | 359 |
BIFURCATIONS | 447 |
CASCADES | 499 |
STATE RECONSTRUCTION FROM DATA | 537 |
A MATRIX ALGEBRA | 557 |
Matrix Times Circle Equals Ellipse | 563 |
ANSWERS AND HINTS TO SELECTED EXERCISES | 577 |
BIBLIOGRAPHY | 587 |
595 | |
Outras edições - Ver todos
Chaos: An Introduction to Dynamical Systems Kathleen T. Alligood,Tim D. Sauer,James A. Yorke Visualização parcial - 2006 |
Chaos: An Introduction to Dynamical Systems Kathleen Alligood,Tim Sauer,J.A. Yorke Visualização parcial - 2012 |
Chaos: An Introduction to Dynamical Systems Kathleen T. Alligood,Tim D. Sauer,James A. Yorke Prévia não disponível - 2000 |
Termos e frases comuns
approximately Assume asymptotically attracting basin behavior bifurcation diagram bifurcation orbit boundary box-counting dimension branch Cantor set cascade cat map chaotic attractor chaotic orbit Chapter contains converge coordinates corresponding crosses curves defined definition denote derivative differential equation disk eigenvalues eigenvector ellipse equilibrium example EXERCISE exists fa(x finite fixed point fractal H´enon map infinite initial conditions initial value integer intersect iterates itinerary Jacobian laser Lemma Let f linear map logistic map Lorenz Lyapunov exponent Lyapunov function Lyapunov number map f matrix measure neighborhood nonlinear one-dimensional maps one-to-one origin parameter value path pendulum period-doubling bifurcation period-k period-three period-two orbit periodic orbit periodic points phase plane plot Poincaré rectangle saddle-node bifurcation sequence shown in Figure shows sink solution stable and unstable Step subintervals subset tent map Theorem torus trajectory transition graph two-dimensional unit interval unit square unstable manifolds unstable orbits vector vertical w-limit set w(vo zero