Potenzialanalysen: Einsatz, methodische Aspekte und Praxisbeispiele

Gourmelon, Andreas; Knabe-Gourmelon, Gudrun

doi:10.5771/9783845219127-397

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The Borel-smale Examples1

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“…Now f B is not dynamically coherent, since E c is not closed under formation of Lie brackets; in fact, [E c , E c ] is spanned by Z 1 and Z 2 . Nicolas Gourmelon has recently shown that it is possible to deform f B in the case a > 0 to obtain a stably ergodic, volume-preserving, partially hyperbolic diffeomorphism that is neither dynamically coherent nor Anosov [10].…”

Section: The Borel-smale Examplesmentioning

confidence: 99%

Dynamical coherence and center bunching

Burns¹,

Wilkinson²

2008

DCDS-A

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Abstract. This paper discusses relationships among the basic notions that have been important in recent investigations of the ergodicity of volume-preserving partially hyperbolic diffeomorphisms. In particular we survey the possible definitions of dynamical coherence and discuss the relationship between dynamical coherence and center bunching.Introduction. Partial hyperbolicity provides a natural context in which the Hopf argument can be used to prove ergodicity. The most recent result in this direction is our theorem:

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Section: The Borel-smale Examplesmentioning

confidence: 99%