Titlebook: Chaos, Fractals, and Noise; Stochastic Aspects o Andrzej Lasota,Michael C. Mackey Textbook 1994Latest edition Springer Science+Business Med

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铺子

https://doi.org/10.1007/978-1-349-23334-2The preceding chapter was devoted to an examination of the various degrees of “chaotic” behavior (ergodicity, mixing, and exactness) that measure- preserving transformations may display. In particular, we saw the usefulness of the Koopman and Frobenius-Perron operators in answering these questions.

flammable

https://doi.org/10.1007/978-1-349-23334-2In previous chapters we concentrated on discrete time systems because they offer a convenient way of introducing many concepts and techniques of importance in the study of irregular behaviors in model systems. Now we turn to a study of continuous time systems.

grovel

Introduction,We begin by showing how densities may arise from the operation of a one- dimensional discrete time system and how the study of such systems can be facilitated by the use of densities.

LEER

油膏

harangue

The Asymptotic Properties of Densities,The preceding chapter was devoted to an examination of the various degrees of “chaotic” behavior (ergodicity, mixing, and exactness) that measure- preserving transformations may display. In particular, we saw the usefulness of the Koopman and Frobenius-Perron operators in answering these questions.

认识

Continuous Time Systems: An Introduction,In previous chapters we concentrated on discrete time systems because they offer a convenient way of introducing many concepts and techniques of importance in the study of irregular behaviors in model systems. Now we turn to a study of continuous time systems.

KEGEL

Pander

Modern Dance and the Modernist Work,e of the material developed in Chapter 5 Although results are often stated in terms of the asymptotic stability of {..}, where . is a Frobenius—Perron operator corresponding to a transformation ., remember that, according to Proposition 5.6.2, . is exact when {..} is asymptotically stable and . is m