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An ergodic theory approach to chaos

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  • This paper is devoted to the ergodic-theoretical approach to chaos, which is based on the existence of invariant mixing measures supported on the whole space. As an example of application of the general theory we prove that there exists an invariant mixing measure with respect to the differentiation operator on the space of entire functions. From this theorem it follows the existence of universal entire functions and other chaotic properties of this transformation.
    Mathematics Subject Classification: Primary: 37L40; Secondary: 28D10, 30D15, 47A16.


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