[en] We show that a fibre-preserving self-diffeomorphism which has hyperbolic splittings along the fibres on a compact principal torus bundle is topologically conjugate to a map that is linear in the fibres.
Disciplines :
Mathematics
Author, co-author :
ZHANG, Danyu ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Department of Mathematics, The Ohio State University, Columbus, United States
External co-authors :
no
Language :
English
Title :
Structural stability for fibrewise Anosov diffeomorphisms on principal torus bundles
C. Bonatti, X. Gómez-Mont and M. Martínez. Foliated hyperbolicity and foliations with hyperbolic leaves. Ergod. Th. & Dynam. Sys. 40(4) (2020), 881–903.
F. T. Farrell and A. Gogolev. On bundles that admit fiberwise hyperbolic dynamics. Math. Ann. 364(1) (2016), 401–438.
J. Franks. Anosov diffeomorphisms on tori. Trans. Amer. Math. Soc. 145 (1969), 117–124.
J. Franks. Anosov diffeomorphisms. Global Anal. 14 (1970), 61–94.
A. Gogolev. Surgery for partially hyperbolic dynamical systems, I: Blow-ups of invariant submanifolds. Geom. Topol. 22(4) (2018), 2219–2252.
A. Gogolev, P. Ontaneda and F. Rodriguez-Hertz. New partially hyperbolic dynamical systems I. Acta Math. 215(2) (2015), 363–393.
A. Hatcher. Algebraic Topology. Cambridge University Press, Cambridge, 2000.
S. Kobayashi and K. Nomizu. Foundations of Differential Geometry. Vol. 1. John Wiley and Sons, New York, 1963.
A. Manning. There are no new anosov diffeomorphisms on tori. Amer. J. Math. 96(3) (1974), 422–429.
R. S. Palais. On the existence of slices for actions of non-compact Lie groups. Ann. of Math. (2) 73(2) (1961), 295–323.
C. Pugh. The closing lemma. Amer. J. Math. 89(4) (1967), 956–1009.
A. Scorpan. The Wild World of 4-Manifolds. American Mathematical Society, Providence, RI, 2005.
