Chaos, Fractals, and Noise: Stochastic Aspects of DynamicsSpringer-Verlag, 1994 - 472 σελίδες In recent years there has been an explosive growth in the study of physical, biological, and economic systems that can be profitably studied using densities. Because of the general inaccessibility of the mathematical literature to the nonspecialist, little diffusion of the applicable mathematics into the study of these "chaotic" systems has taken place. This book will help bridge that gap. To show how densities arise in simple deterministic systems, the authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial-differential equations. Examples have been drawn from many fields to illustrate the utility of the concepts and techniques presented, and the ideas in this book should thus prove useful in the study of a number of applied sciences. The authors assume that the reader has a knowledge of advanced calculus and differential equations. Basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed. Physicists, chemists, and biomathematicians studying chaotic behavior will find this book of value. It will also be a useful reference or text for mathematicians and graduate students working in ergodic theory and dynamical systems. |
Περιεχόμενα
Introduction | 1 |
The Toolbox | 17 |
Markov and FrobeniusPerron Operators | 37 |
Πνευματικά δικαιώματα | |
14 άλλες ενότητες δεν εμφανίζονται
Άλλες εκδόσεις - Προβολή όλων
Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics Andrzej Lasota,Michael C. Mackey Περιορισμένη προεπισκόπηση - 1998 |
Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics Andrzej Lasota,Michael C. Mackey Περιορισμένη προεπισκόπηση - 2013 |
Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics Andrzej Lasota,Michael C. Mackey Προβολή αποσπασμάτων - 1994 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ absolutely continuous arbitrary assume asymptotically periodic asymptotically stable B₁ baker transformation behavior Borel measure bounded compact support completes the proof consider constant Corollary defined definition denotes density f derivative differential equations dyadic transformation dynamical system entropy ergodic exact Example exists Figure finite measure Fokker-Planck equation formula Frobenius-Perron operator corresponding function f given implies independent inequality infinitesimal operator initial condition interval iterates Itô Koopman operator L¹(X Lebesgue integral limit lower-bound function mapping Markov operator measure space nonnegative nonsingular o-algebra obtain perturbation Pf(x precompact probabilistic properties Proposition prove random variables random vector Remark result right-hand side satisfies semidynamical system semigroup sequence solution stationary density stochastic kernel stochastic process stochastic semigroup strong convergence subset sweeping trajectory unique Wiener process µ(dx