Titlebook: Concepts and Results in Chaotic Dynamics: A Short Course; Pierre Collet,Jean-Pierre Eckmann Textbook 2006 Springer-Verlag Berlin Heidelber

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Invariant Measures,We start by giving a brief overview of some ideas and results to which we will come back later in detail.

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Ambulatory

Other Probabilistic Results,A number of questions of probabilistic origin have been investigated in the class of stochastic processes generated by dynamical systems. We describe some of the results below.

CHYME

Pierre Collet,Jean-Pierre EckmannIncludes supplementary material:

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Theoretical and Mathematical Physicshttp://image.papertrans.cn/c/image/234908.jpg

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Outline of the CMEA Game-theoretic Designlize this. One formalization will be based on partitioning the phase space into pieces and considering that the experiment will only tell us in which piece of the partition (called an atom) a point currently is, but not where inside this piece it happens to be. This is analogous to classical coarse-

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https://doi.org/10.1007/BFb0058648 also connect it to the notion of invariant measure. That is, we account (in particular in the natural case of the Physical measure) for how often (or how long) a trajectory stays in a particular region. One can ask how much information this gives us about the long-time dynamics of the system and th

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Controllability of multidimensional systems, knowing whether the necessary mathematical assumptions are satisfied by a given system. But it turns out that it is very useful, in concrete examples, to act “as if” they were true. We do not enter into the many details which have been studied in the experimental-theoretical literature, such as opt

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1864-5879 ior in time of maps and ?ows, called dynamical systems. The theory of chaotic dynamics has a deep impact on our understanding of - ture, and we sketch here our view on this question. The strength of this theory comes from its generality, in that it is not limited to a particular equation or scienti?