Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 741–755 | Cite as

Properties of compact center-stable submanifolds

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Abstract

We show that a partially hyperbolic system can have at most a finite number of compact center-stable submanifolds. We also give sufficient conditions for these submanifolds to exist and consider the question of whether they can intersect each other.

Keywords

Partial hyperbolicity Attractors Center-stable submanifolds 

Mathematics Subject Classification

37D30 37C70 

Notes

Acknowledgements

The author thanks Rafael Potrie for beneficial conversations and the anonymous reviewer for helpful comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesMonash UniversityVictoriaAustralia

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