An ergodic theory approach to chaos

Ryszard Rudnicki

doi:10.3934/dcds.2015.35.757

Article Contents

2015, Volume 35, Issue 2: 757-770. Doi: 10.3934/dcds.2015.35.757

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An ergodic theory approach to chaos

Ryszard Rudnicki^1,

1.
Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice

Received: January 31, 2013

Revised: September 30, 2013

Published: January 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 37L40; Secondary: 28D10, 30D15, 47A16.

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