Indices of singularities of robustly transitive sets

Shengzhi Zhu; Shaobo Gan; Lan Wen

doi:10.3934/dcds.2008.21.945

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2008, Volume 21, Issue 3: 945-957. Doi: 10.3934/dcds.2008.21.945

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Indices of singularities of robustly transitive sets

1.
School of Mathematical Science, Peking University, Beijing 100871
2.
School of Mathematic Sciences, Peking University, Beijing, 100871

Received: July 31, 2007

Revised: December 31, 2007

Published: August 2008

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Abstract

It was proved recently in [4] that any robustly transitive singular set that is strongly homogenous must be partially hyperbolic, as long as the indices of singularities and periodic orbits satisfy certain condition. We prove in this paper that this index-condition is automatically satisfied under the strongly homogenous condition, hence can be removed from the assumptions. Moreover, we prove that a robustly transitive singular set that is strongly homogenous is in fact singular hyperbolic.

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Mathematics Subject Classification: 37D30.

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