Topological Anosov maps of infra-nil-manifolds

Naoya SUMI

doi:10.2969/jmsj/04840607

Naoya SUMI

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JOURNAL FREE ACCESS

1996 Volume 48 Issue 4 Pages 607-648

DOI https://doi.org/10.2969/jmsj/04840607

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Published: 1996 Received: April 12, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : An) D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math., 90 (1967), 1-235.
Ao-Hi) N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, Mathematical Library, North Holland, 1994.
Au) L. Auslander, Bieberbach's theorems on space groups and discrete uniform subgroups of Lie groups, Ann. of Math., 71 (1960), 579-590.
Co-Re) E. Coven and W. Reddy, Positively expansive maps of compact manifolds, Lecture Notes in Math., 819. Springer-Verlag, 1980, pp. 96-110.
Fr) J. Franks, Anosov diffeomorphisms, Global Analysis, Proc. Sympos. Pure Math., 14 (1970), 61-93.
Gr) M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES, 53 (1981), 53-78.
Hi 1) K. Hiraide, Positively expansive open maps of Peano spaces, Topology Appl.. 37 (1990), 213-220.
Hi 2) K. Hiraide, On an ordering of dynamics of homeomorphisms, preprint.
Ma-Pu) R. Mañé and C. Pugh, Stability of endomorphisms, Lecture Notes in Math., 468, Springer-Verlag, 1975, pp. 175-184.
Ma 1) A. Manning, Anosov diffeomorphisms on nilmanifolds, Proc. Amer. Math. Soc., 38 (1973), 423-426.
Ma 2) A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429,
Pa) W. Parry, Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math., 91 (1969), 757-771.
Pr) F. Przytycki, Anosov endomorphisms, Studia Math., 58 (1976), 249-285.
Re) W. Reddy, Expanding maps on compact metric spaces, Topology Appl., 13 (1982), 327-334.
Sh) M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math., 91 (1969), 175-199.
Sm) S. Smale, Differential dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
Su) N. Sumi, Linearization of expansive maps of tori, Proc. of International Conference on Dynamical Systems and Chaos, 1 (1994), 243-248.
Va) V.S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, GTM. 102, Springer-Verlag, New York, 1984.
Wo) J. A. Wolf, Spaces of Constant Curvature, McGraw-Hill, 1967.

Right : [An] D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math., 90 (1967), 1-235.
[Ao-Hi] N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, Mathematical Library, North Holland, 1994.
[Au] L. Auslander, Bieberbach's theorems on space groups and discrete uniform subgroups of Lie groups, Ann. of Math., 71 (1960), 579-590.
[Co-Re] E. Coven and W. Reddy, Positively expansive maps of compact manifolds, Lecture Notes in Math., 819. Springer-Verlag, 1980, pp. 96-110.
[Fr] J. Franks, Anosov diffeomorphisms, Global Analysis, Proc. Sympos. Pure Math., 14 (1970), 61-93.
[Gr] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES, 53 (1981), 53-78.
[Hi 1] K. Hiraide, Positively expansive open maps of Peano spaces, Topology Appl.. 37 (1990), 213-220.
[Hi 2] K. Hiraide, On an ordering of dynamics of homeomorphisms, preprint.
[Ma-Pu] R. Mañé and C. Pugh, Stability of endomorphisms, Lecture Notes in Math., 468, Springer-Verlag, 1975, pp. 175-184.
[Ma 1] A. Manning, Anosov diffeomorphisms on nilmanifolds, Proc. Amer. Math. Soc., 38 (1973), 423-426.
[Ma 2] A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429,
[Pa] W. Parry, Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math., 91 (1969), 757-771.
[Pr] F. Przytycki, Anosov endomorphisms, Studia Math., 58 (1976), 249-285.
[Re] W. Reddy, Expanding maps on compact metric spaces, Topology Appl., 13 (1982), 327-334.
[Sh] M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math., 91 (1969), 175-199.
[Sm] S. Smale, Differential dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
[Su] N. Sumi, Linearization of expansive maps of tori, Proc. of International Conference on Dynamical Systems and Chaos, 1 (1994), 243-248.
[Va] V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, GTM. 102, Springer-Verlag, New York, 1984.
[Wo] J. A. Wolf, Spaces of Constant Curvature, McGraw-Hill, 1967.

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