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Robust special Anosov endomorphisms

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In this paper we introduce the notion of \emph{``robust special \linebreak Anosov endomorphisms"}, and show that Anosov endomorphisms of tori which are not neither an Anosov diffeomorphism nor an expanding map, are not robust special.

Abstract

In this paper we introduce the notion of \emph{``robust special \linebreak Anosov endomorphisms"}, and show that Anosov endomorphisms of tori which are not neither an Anosov diffeomorphism nor an expanding map, are not robust special.

참고문헌 (12)

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  3. Louis Auslander, "Bieberbach's Theorems on Space Groups and Discrete Uniform Subgroups of Lie Groups", The Annals of Mathematics, 71(3), pp.579~ (1960), JSTOR[DOI]
  4. K. Dekimpe, "What is ... an infra-nilmanifold endomorphism?", Notices Amer. Math. Soc, 58(5), pp.688~689 (2011)
  5. K. Dekimpe, "What an infra-nilmanifold endomorphism really should be...", Topol. Meth-ods Nonlinear Anal, 40(1), pp.111~136 (2012)
  6. R. Mane, "Stability of endomorphisms, in Dynamical systems|Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ.Warwick, Coventry, 1973", 1974; presented to E. C. Zeeman on his ftieth birthday), 175-184, 1975, pp.468, ~[DOI]
  7. Fernando Micena, "On the unstable directions and Lyapunov exponents of Anosov endomorphisms", Fundamenta Mathematicae, pp.1~12 (2016), Institute of Mathematics, Polish Academy of Sciences[DOI]
  8. S. M. Moosavi, "Classication of special Anosov endomorphisms of nil-manifolds", Acta Mathematica Sinica
  9. Feliks Przytycki, "Anosov endomorphisms", Studia Mathematica, 58(3), pp.249~285 (1976), Institute of Mathematics, Polish Academy of Sciences[DOI]
  10. Michael Shub, "Endomorphisms of Compact Differentiable Manifolds", American Journal of Mathematics, 91(1), pp.175~ (1969), JSTOR[DOI]
  11. N. Sumi, "Topological Anosov maps of infra-nil-manifolds", J. Math. Soc. Japan, 48(4), pp.607~648 (1996)[DOI]
  12. M. R. Zhang, "On the topologically conjugate classes of Anosov endomorphisms on tori", Chinese Ann. Math. Ser. B, 10(3), pp.416~425 (1989)

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