The nonexistence of expansive homeomorphisms of Suslinian continua

Hisao KATO

doi:10.2969/jmsj/04240631

Hisao KATO

著者情報

ジャーナルフリー

1990 年 42 巻 4 号 p. 631-637

DOI https://doi.org/10.2969/jmsj/04240631

詳細

Published: 1990 Received: 1989/05/29 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Ryosuke Nakagawa on his 60th birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) B. F. Bryant, Unstable self-homeomorphisms of a compact space, Vanderbilt University, Thesis, 1954.
2) H. Cook and A. Lelek, Weakly confluent mappings and atriodic Suslinian curves, Canad. J. Math., 30 (1978), 32-44.
3) M. Dateyama, Some class of one-dimensional dynamical systems without expansiveness, preprint.
4) J. F. Jacobson and W. R. Utz, The nonexistence of expansive homeomorphisms of a closed 2-cell, Pacific J. Math., 10 (1960), 1319-1321.
5) K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo Anosov, Osaka J. Math., to appear.
6) H. Kato, The nonexistence of expansive homeomorphisms of 1-dimensional compact ANRs, Proc. Amer. Math. Soc., 108 (1990), 267-269.
7) H. Kato, The nonexistence of expansive homeomorphisms of Peano continua in the plane, Topology Appl., 34 (1990), 161-165.
8) H. Kato, The nonexistence of expansive homeomorphisms of dendroids, Fund. Math., to appear.
9) H. Kato, Expansive homeomorphisms, Kokyuroku, Res. Inst. Math. Kyoto University (in Japanese), 711 (1989), 68-85.
10) H. Kato and K. Kawamura, A class of continua which admit no expansive homeomorphisms, Rocky Mountain J. Math., to appear.
11) K. Kawamura, A direct proof that Peano continuum with a free arc admits no expansive homeomorphisms, Tsukuba J. Math., 12 (1988), 521-524.
12) R. Mañé, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc., 252 (1979), 313-319.
13) T. O'Brien and W. Reddy, Each compact orientable surface of positive genus admits an expansive homeomorphism, Pacific J. Math., 35 (1970), 737-741.
14) R. F. Williams, A note on unstable homeomorphisms, Proc. Amer. Math. Soc., 6 (1955), 308-309.
15) M. Barge, Personal communication.
16) M. Eisenberg, A note on positively expansive endomorphisms, Math. Scand., 19 (1966), 217-218.
17) N. Aoki, M. Dateyama and M. Komuro, Solenoidal automorphisms with specifications, Monatsh. Math., 93 (1982), 79-110.
18) N. Aoki and M. Dateyama, The relationship between algebraic numbers and expansiveness of automorphisms on compact abelian groups, Fund. Math., 117 (1983), 21-35.

Right : [1] B. F. Bryant, Unstable self-homeomorphisms of a compact space, Vanderbilt University, Thesis, 1954.
[2] H. Cook and A. Lelek, Weakly confluent mappings and atriodic Suslinian curves, Canad. J. Math., 30 (1978), 32-44.
[3] M. Dateyama, Some class of one-dimensional dynamical systems without expansiveness, preprint.
[4] J. F. Jacobson and W. R. Utz, The nonexistence of expansive homeomorphisms of a closed 2-cell, Pacific J. Math., 10 (1960), 1319-1321.
[5] K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo Anosov, Osaka J. Math., to appear.
[6] H. Kato, The nonexistence of expansive homeomorphisms of 1-dimensional compact ANRs, Proc. Amer. Math. Soc., 108 (1990), 267-269.
[7] H. Kato, The nonexistence of expansive homeomorphisms of Peano continua in the plane, Topology Appl., 34 (1990), 161-165.
[8] H. Kato, The nonexistence of expansive homeomorphisms of dendroids, Fund. Math., to appear.
[9] H. Kato, Expansive homeomorphisms, Kokyuroku, Res. Inst. Math. Kyoto University (in Japanese), 711 (1989), 68-85.
[10] H. Kato and K. Kawamura, A class of continua which admit no expansive homeomorphisms, Rocky Mountain J. Math., to appear.
[11] K. Kawamura, A direct proof that Peano continuum with a free arc admits no expansive homeomorphisms, Tsukuba J. Math., 12 (1988), 521-524.
[12] R. Mañé, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc., 252 (1979), 313-319.
[13] T. O'Brien and W. Reddy, Each compact orientable surface of positive genus admits an expansive homeomorphism, Pacific J. Math., 35 (1970), 737-741.
[14] R. F. Williams, A note on unstable homeomorphisms, Proc. Amer. Math. Soc., 6 (1955), 308-309.
[15] M. Barge, Personal communication.
[16] M. Eisenberg, A note on positively expansive endomorphisms, Math. Scand., 19 (1966), 217-218.
[17] N. Aoki, M. Dateyama and M. Komuro, Solenoidal automorphisms with specifications, Monatsh. Math., 93 (1982), 79-110.
[18] N. Aoki and M. Dateyama, The relationship between algebraic numbers and expansiveness of automorphisms on compact abelian groups, Fund. Math., 117 (1983), 21-35.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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