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Equivariant Diffeomorphisms Hyperbolic Transverse to a G ‐Action
Author(s) -
Field M. J.
Publication year - 1983
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-27.3.563
Subject(s) - equivariant map , diffeomorphism , mathematics , action (physics) , pure mathematics , lie group , manifold (fluid mechanics) , subspace topology , group (periodic table) , dimension (graph theory) , differential (mechanical device) , transverse plane , group action , mathematical analysis , physics , quantum mechanics , mechanical engineering , structural engineering , engineering , thermodynamics
Let G be a compact Lie group acting smoothly on a compact differential manifold and suppose that all G ‐orbits have the same dimension. We say that a G ‐equivariant diffeomorphism is G ‐Anosov if it is hyperbolic transverse to the G ‐action. We prove that G ‐Anosov diffeomorphisms are G ‐structurally stable and form an open subspace of the group of equivariant diffeomorphisms. We prove similar results for flows.