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Korean Mathematical Society
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ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2005; 42(4): 857-869

Printed July 1, 2005

Copyright © The Korean Mathematical Society.

Relative sequence entropy pairs for a measure and relative topological Kronecker factor

Young-Ho Ahn, Jungseob Lee, and Kyewon Koh Park

Mokpo National University, Ajou University, Ajou University

Abstract

Let $(X, \mathcal B, \mu , T)$ be a dynamical system and $(Y, \mathcal A,\nu ,S)$ be a factor. We investigate the relative sequence entropy of a partition of $X$ via the maximal compact extension of $(Y, \mathcal A,\nu , S)$. We define relative sequence entropy pairs and using them, we find the relative topological $\mu$-Kronecker factor over $(Y, \nu)$ which is the maximal topological factor having relative discrete spectrum over $(Y, \nu)$. We also describe the topological Kronecker factor which is the maximal factor having discrete spectrum for any invariant measure.

Keywords: relative sequence entropy, relative sequence entropy pairs, relative weakly mixing, compact extension, relative Kronecker factor, equicontinuous factor, null factor

MSC numbers: 28D05, 47A35

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