Expansive homeomorphisms with the pseudo-orbit tracing property of n-tori

Koichi HIRAIDE

doi:10.2969/jmsj/04130357

Koichi HIRAIDE

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 3 Pages 357-389

DOI https://doi.org/10.2969/jmsj/04130357

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Published: 1989 Received: October 12, 1987 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: SUBTITLE Details: Wrong : Dedicated to Professor Yukihiro Kodama on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Aoki, On homeomorphisms with pseudo-orbit tracing property, Tokyo J. Math., 6 (1983), 329-334.
2) N. Aoki and K. Hiraide, Generalized foliations and algebraic representations of maps on dynamical systems, preprint.
3) R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math., 470, Springer, 1975.
4) G. Bredon, Sheaf Theory, McGraw-Hill, New York, 1967.
5) M. Brin and A. Manning, Anosov diffeomorphisms with pinched spectrum, Lecture Notes in Math., 898, Springer, 1981, pp. 48-53.
6) R. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresmann and Company, 1971.
7) A. Dold, Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology, 4 (1965), 1-8.
8) P. Duvall and L. Husch, Analysis on topological manifolds, Fund. Math., 77 (1972) 75-90.
9) J. Franks, Anosov diffeomorphisms on tori, Trans. Amer. Math. Soc., 145 (1969), 117-124.
10) J. Franks, Anosov diffeomorphisms, Global Analysis, Proc. Sympos. Pure Math., 14 (1970), Amer. Math. Soc., 61-93.
11) K. Hiraide, On homeomorphisms with Markov partitions, Tokyo J. Math., 8 (1985), 219-229.
12) K. Hiraide, Expansive homeomorphisms with the pseudo-orbit tracing property on compact surfaces, J. Math. Soc. Japan, 40 (1988), 123-137.
13) K. Hiraide, Expansive homeomorphisms with the pseudo-orbit tracing property of n-tori, Dynamical Systems and Applications, World Sci. Publ., Singapore, 1987, pp. 35-41.
14) R. Mañé, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc., 252 (1979), 313-319.
15) A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429.
16) A. Morimoto, The method of pseudo-orbit tracing and stability of dynamical systems, Seminar Note, 39, Dept. Math. Tokyo Univ., 1979, (in Japanese).
17) E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.

Right : [1] N. Aoki, On homeomorphisms with pseudo-orbit tracing property, Tokyo J. Math., 6 (1983), 329-334.
[2] N. Aoki and K. Hiraide, Generalized foliations and algebraic representations of maps on dynamical systems, preprint.
[3] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math., 470, Springer, 1975.
[4] G. Bredon, Sheaf Theory, McGraw-Hill, New York, 1967.
[5] M. Brin and A. Manning, Anosov diffeomorphisms with pinched spectrum, Lecture Notes in Math., 898, Springer, 1981, pp. 48-53.
[6] R. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresmann and Company, 1971.
[7] A. Dold, Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology, 4 (1965), 1-8.
[8] P. Duvall and L. Husch, Analysis on topological manifolds, Fund. Math., 77 (1972) 75-90.
[9] J. Franks, Anosov diffeomorphisms on tori, Trans. Amer. Math. Soc., 145 (1969), 117-124.
[10] J. Franks, Anosov diffeomorphisms, Global Analysis, Proc. Sympos. Pure Math., 14 (1970), Amer. Math. Soc., 61-93.
[11] K. Hiraide, On homeomorphisms with Markov partitions, Tokyo J. Math., 8 (1985), 219-229.
[12] K. Hiraide, Expansive homeomorphisms with the pseudo-orbit tracing property on compact surfaces, J. Math. Soc. Japan, 40 (1988), 123-137.
[13] K. Hiraide, Expansive homeomorphisms with the pseudo-orbit tracing property of n-tori, Dynamical Systems and Applications, World Sci. Publ., Singapore, 1987, pp. 35-41.
[14] R. Mañé, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc., 252 (1979), 313-319.
[15] A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429.
[16] A. Morimoto, The method of pseudo-orbit tracing and stability of dynamical systems, Seminar Note, 39, Dept. Math. Tokyo Univ., 1979, (in Japanese).
[17] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.

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