Equivalent conditions of dominated splitting for volume-preserving diffeomorphisms

DOI10.1007/S10114-005-0889-6zbMath1129.37011OpenAlexW2060715379MaRDI QIDQ2463795

Geng Liu, Chao Liang, Wen Xiang Sun

Publication date: 6 December 2007

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0889-6

zbMATH Keywords

dominated splittinghomoclinic tangencyvolume-preserving diffeomorphismpreperiodic point

Mathematics Subject Classification ID

Partially hyperbolic systems and dominated splittings (37D30)

Related Items (6)

Conditions for dominated splittings ⋮ A lower bound for topological entropy of generic non-Anosov symplectic diffeomorphisms ⋮ New derived from Anosov diffeomorphisms with pathological center foliation ⋮ Dominated splitting versus small angles ⋮ Pathological center foliation with dimension greater than one ⋮ Hyperbolicity in the volume-preserving scenario

Cites Work

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• Quadratic forms and Steenrod squares
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
• An ergodic closing lemma
• Homoclinic points in symplectic and volume-preserving diffeomorphisms
• The C¹ closing lemma for non-singular endomorphisms
• Quasi-Anosov Diffeomorphisms and Hyperbolic Manifolds
• Homoclinic tangencies and dominated splittings

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