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August  2008, 21(3): 945-957. doi: 10.3934/dcds.2008.21.945

Indices of singularities of robustly transitive sets

Shengzhi Zhu 1, , Shaobo Gan 1, and  Lan Wen 2,

1. 

School of Mathematical Science, Peking University, Beijing 100871, China
2. 

School of Mathematic Sciences, Peking University, Beijing, 100871

Received  August 2007 Revised  January 2008 Published  April 2008

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.
Keywords: Strongly homogenous, robustly transitive, singular hyperbolic..
Mathematics Subject Classification: 37D3.
Citation: Shengzhi Zhu, Shaobo Gan, Lan Wen. Indices of singularities of robustly transitive sets. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 945-957. doi: 10.3934/dcds.2008.21.945
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