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

Absenteeism

Looking Beyond Form: Foreman, Kirby, Wilson, space. To do this, we adopt a strictly probabilistic point of view, not embedding the deterministic system . in a continuous time process, but rather embedding its Frobenius-Perron operator ..... that acts on .. functions. The result of this embedding is an abstract form of the Boltzmann equation.

MENT

BOON

Modern Dance and the Modernist Work,ence of following a random distribution of initial states, which, in turn, led to a development of the notion of the Frobenius-Perron operator and an examination of its properties as a means of studying the asymptotic properties of flows of densities. The second resulted from the random application

有恶臭

https://doi.org/10.1007/978-1-349-23334-2 and to a derivation of the forward Fokker-Planck equation, describing the evolution of densities for these systems. We close with some results concerning the asymptotic stability of solutions to the Fokker-Planck equation.

辩论

From Postmodern Style to Performance,better described if we use a more general notion than a density, namely, a measure. In fact, the sequences (or flows) of measures generated by dynamical systems simultaneously generalize the notion of trajectories and the sequences (or flows) of densities. They are of particular value in studying fr

CRAFT

Studying Chaos with Densities,ormations can display. These three levels are known as ergodicity, mixing, and exactness. The central theme of the chapter is to show the utility of the Frobenius–Perron and Koopman operators in the study of these behaviors.

抛媚眼

The Behavior of Transformations on Intervals and Manifolds,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 measure preserving.

粗糙滥制

Stochastic Perturbation of Continuous Time Systems, and to a derivation of the forward Fokker-Planck equation, describing the evolution of densities for these systems. We close with some results concerning the asymptotic stability of solutions to the Fokker-Planck equation.

BUCK

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