Chaos, Fractals, and Noise: Stochastic Aspects of DynamicsSpringer Science & Business Media, 27 Νοε 2013 - 474 σελίδες The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter. |
Περιεχόμενα
1 | |
The Toolbox 17 | 16 |
Markov and FrobeniusPerron Operators | 37 |
Studying Chaos with Densities | 51 |
1 | 86 |
6 | 137 |
1 | 176 |
An Introduction | 189 |
7 | 215 |
Discrete Time Processes Embedded in Continuous | 250 |
Entropy | 283 |
Stochastic Perturbation of Discrete Time Systems 303 | 302 |
Stochastic Perturbation of Continuous Time Systems | 335 |
Markov and Foias Operators | 393 |
449 | |
Notation and Symbols | 457 |
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 Προβολή αποσπασμάτων - 1994 |
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 baker transformation behavior Borel measure bounded compact support 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 Hille-Yosida theorem implies independent inequality infinitesimal operator initial condition interval iterates Itô Koopman operator L¹(X Lebesgue integral limit linear lower-bound function mapping Markov operator measure space nonnegative nonsingular obtain 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 supp sweeping trajectory unique Wiener process µ(dx მე