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Volumn 93, Issue , 2004, Pages 103-138

Structure of three-interval exchange transformations III: Ergodic and spectral properties

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EID: 10044248295     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/BF02789305     Document Type: Article
Times cited : (28)

References (37)
  • 1
    • 0000787759 scopus 로고
    • Un exemple de semi-conjugaison entre un échange d'intervalles et une translation sur le tore
    • P. Arnoux, Un exemple de semi-conjugaison entre un échange d'intervalles et une translation sur le tore, Bull. Soc. Math. France 116 (1988), 489-500.
    • (1988) Bull. Soc. Math. France , vol.116 , pp. 489-500
    • Arnoux, P.1
  • 2
    • 85009730418 scopus 로고    scopus 로고
    • The scenery flow for geometric structures on the torus: The linear setting
    • P. Arnoux and A. M. Fischer, The scenery flow for geometric structures on the torus: the linear setting, Chinese Ann. Math. Ser. B 22 (2001), 427-470.
    • (2001) Chinese Ann. Math. Ser. B , vol.22 , pp. 427-470
    • Arnoux, P.1    Fischer, A.M.2
  • 3
    • 0001764604 scopus 로고
    • Représentation géométrique de suites de complexité 2n + 1
    • P. Arnoux and G. Rauzy, Représentation géométrique de suites de complexité 2n + 1, Bull. Soc. Math. France 119 (1991), 199-215.
    • (1991) Bull. Soc. Math. France , vol.119 , pp. 199-215
    • Arnoux, P.1    Rauzy, G.2
  • 4
    • 0040038451 scopus 로고    scopus 로고
    • Covering numbers: Arithmetics and dynamics for rotations and interval exchanges
    • V. Berthé, N. Chekhova and S. Ferenczi, Covering numbers: arithmetics and dynamics for rotations and interval exchanges, J. Analyse Math. 79 (1999), 1-31.
    • (1999) J. Analyse Math. , vol.79 , pp. 1-31
    • Berthé, V.1    Chekhova, N.2    Ferenczi, S.3
  • 5
    • 84972546502 scopus 로고
    • A condition for minimal interval exchange maps to be uniquely ergodic
    • M. Boshernitzan, A condition for minimal interval exchange maps to be uniquely ergodic. Duke Math. J. 52 (1985), 723-752.
    • (1985) Duke Math. J. , vol.52 , pp. 723-752
    • Boshernitzan, M.1
  • 7
    • 0005580873 scopus 로고    scopus 로고
    • An extension of Lagrange's Theorem to interval exchange transformations over quadratic fields
    • M. Boshernitzan and C. R. Carroll, An extension of Lagrange's Theorem to interval exchange transformations over quadratic fields, J. Analyse Math. 72 (1997), 21-44.
    • (1997) J. Analyse Math. , vol.72 , pp. 21-44
    • Boshernitzan, M.1    Carroll, C.R.2
  • 10
    • 0039251878 scopus 로고    scopus 로고
    • Spectral properties of interval exchange maps
    • J. Chaves and A. Nogueira, Spectral properties of interval exchange maps, Monatsh. Math. 134 (2001), 89-102.
    • (2001) Monatsh. Math. , vol.134 , pp. 89-102
    • Chaves, J.1    Nogueira, A.2
  • 11
    • 0009032286 scopus 로고
    • The group of eigenvalues of a rank-one transformation
    • J. R. Choksi and M. G. Nadkarni, The group of eigenvalues of a rank-one transformation, Canad. Math. Bull. 38 (1995), 42-54.
    • (1995) Canad. Math. Bull. , vol.38 , pp. 42-54
    • Choksi, J.R.1    Nadkarni, M.G.2
  • 13
    • 0000060895 scopus 로고
    • Sequences with minimal block growth
    • E. M. Coven and G. A. Hedlund, Sequences with minimal block growth. Math. Systems Theory 7 (1972), 138-153.
    • (1972) Math. Systems Theory , vol.7 , pp. 138-153
    • Coven, E.M.1    Hedlund, G.A.2
  • 14
    • 0010860931 scopus 로고
    • A family of counterexamples in ergodic theory
    • A. del Junco, A family of counterexamples in ergodic theory, Israel J. Math. 44 (1983), 160-188.
    • (1983) Israel J. Math. , vol.44 , pp. 160-188
    • Del Junco, A.1
  • 16
    • 0002973775 scopus 로고    scopus 로고
    • Systems of finite rank
    • S. Ferenczi, Systems of finite rank, Colloq. Math. 73 (1997), 35-65.
    • (1997) Colloq. Math. , vol.73 , pp. 35-65
    • Ferenczi, S.1
  • 17
    • 0001149248 scopus 로고    scopus 로고
    • Transcendence of numbers with a low complexity expansion
    • S. Ferenczi and C. Mauduit, Transcendence of numbers with a low complexity expansion, J. Number Theory 67 (1997), 146-161.
    • (1997) J. Number Theory , vol.67 , pp. 146-161
    • Ferenczi, S.1    Mauduit, C.2
  • 18
    • 0035623014 scopus 로고    scopus 로고
    • The structure of three-interval exchange transformations I: An arithmetic study
    • S. Ferenczi, C. Holton and L. Zamboni, The structure of three-interval exchange transformations I: an arithmetic study, Ann. Inst. Fourier (Grenoble) 51 (2001), 861-901.
    • (2001) Ann. Inst. Fourier (Grenoble) , vol.51 , pp. 861-901
    • Ferenczi, S.1    Holton, C.2    Zamboni, L.3
  • 19
    • 7544231828 scopus 로고    scopus 로고
    • The structure of three-interval exchange transformations II: A combinatorial description of the trajectories
    • S. Ferenczi, C. Holton and L. Zamboni, The structure of three-interval exchange transformations II: a combinatorial description of the trajectories, J. Analyse Math. 89 (2003), 239-276.
    • (2003) J. Analyse Math. , vol.89 , pp. 239-276
    • Ferenczi, S.1    Holton, C.2    Zamboni, L.3
  • 20
    • 0001834320 scopus 로고
    • Approximations in ergodic theory
    • (in Russian)
    • A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Usp. Mat. Nauk 22 (1967), 81-106 (in Russian), translated in Russian Math. Surveys 22 (1967), 76-102.
    • (1967) Usp. Mat. Nauk , vol.22 , pp. 81-106
    • Katok, A.B.1    Stepin, A.M.2
  • 21
    • 0040078342 scopus 로고
    • A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Usp. Mat. Nauk 22 (1967), 81-106 (in Russian), translated in Russian Math. Surveys 22 (1967), 76-102.
    • (1967) Russian Math. Surveys , vol.22 , pp. 76-102
  • 22
    • 0002772850 scopus 로고
    • Interval exchange transformations
    • M. S. Keane, Interval exchange transformations, Math. Z. 141 (1975), 25-31.
    • (1975) Math. Z. , vol.141 , pp. 25-31
    • Keane, M.S.1
  • 23
    • 0000511668 scopus 로고
    • Non-ergodic internal exchange transformations
    • M. S. Keane, Non-ergodic internal exchange transformations, Israel J. Math. 26 (1977), 188-196.
    • (1977) Israel J. Math. , vol.26 , pp. 188-196
    • Keane, M.S.1
  • 24
    • 0039608783 scopus 로고
    • A "minimal" non-uniquely ergodic interval exchange transformation
    • H. Keynes and D. Newton, A "minimal" non-uniquely ergodic interval exchange transformation, Math. Z. 148 (1976), 101-106.
    • (1976) Math. Z. , vol.148 , pp. 101-106
    • Keynes, H.1    Newton, D.2
  • 25
    • 0000742775 scopus 로고
    • Interval exchange transformations and measured foliations
    • H. Masur, Interval exchange transformations and measured foliations, Ann. of Math. 115 (1982), 169-200.
    • (1982) Ann. of Math. , vol.115 , pp. 169-200
    • Masur, H.1
  • 26
    • 51249174077 scopus 로고
    • Cohomology of step functions under irrational rotations
    • K. D. Merrill, Cohomology of step functions under irrational rotations, Israel J. Math. 52 (1985), 320-340.
    • (1985) Israel J. Math. , vol.52 , pp. 320-340
    • Merrill, K.D.1
  • 27
    • 0001788272 scopus 로고
    • Symbolic dynamics II. Sturmian trajectories
    • M. Morse and G. A Hedlund, Symbolic dynamics II. Sturmian trajectories. Amer. J. Math. 62 (1940), 1-42.
    • (1940) Amer. J. Math. , vol.62 , pp. 1-42
    • Morse, M.1    Hedlund, G.A.2
  • 28
    • 0039768869 scopus 로고    scopus 로고
    • Topological weak-mixing of interval exchange maps
    • A. Nogueira and D. Rudolph, Topological weak-mixing of interval exchange maps, Ergodic Theory Dynam. Systems 17 (1997), 1183-1209.
    • (1997) Ergodic Theory Dynam. Systems , vol.17 , pp. 1183-1209
    • Nogueira, A.1    Rudolph, D.2
  • 29
    • 0000958995 scopus 로고
    • Échanges
    • G. Rauzy, Échanges d'intervalles et transformations induites, Acta Arith. 34 (1979), 315-328.
    • (1979) Acta Arith. , vol.34 , pp. 315-328
    • Rauzy, G.1
  • 30
    • 0010074422 scopus 로고
    • Irregularities of uniform distribution
    • M. Stewart, Irregularities of uniform distribution, Acta Math. Acad. Sci. Hungar. 37 (1981), 185-221.
    • (1981) Acta Math. Acad. Sci. Hungar. , vol.37 , pp. 185-221
    • Stewart, M.1
  • 31
    • 33744817583 scopus 로고
    • Strict ergodicity in zero dimensional dynamical systems and the Kronecker-Weyl theorem mod 2
    • W. A. Veech, Strict ergodicity in zero dimensional dynamical systems and the Kronecker-Weyl theorem mod 2, Trans. Amer. Math. Soc. 140 (1969), 1-33.
    • (1969) Trans. Amer. Math. Soc. , vol.140 , pp. 1-33
    • Veech, W.A.1
  • 32
    • 51249180903 scopus 로고
    • Interval exchange transformations
    • W. A. Veech, Interval exchange transformations, J. Analyse Math. 33 (1978), 222-272.
    • (1978) J. Analyse Math. , vol.33 , pp. 222-272
    • Veech, W.A.1
  • 33
    • 10044293414 scopus 로고
    • Projective Swiss cheeses and uniquely ergodic interval exchange transformation
    • W. A. Veech, Projective Swiss cheeses and uniquely ergodic interval exchange transformation, Progr. Math. 10 (1981), 113-193.
    • (1981) Progr. Math. , vol.10 , pp. 113-193
    • Veech, W.A.1
  • 34
    • 0000742776 scopus 로고
    • Gauss measures for transformations on the space of interval exchange maps
    • W. A. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. 115 (1982), 201-242.
    • (1982) Ann. of Math. , vol.115 , pp. 201-242
    • Veech, W.A.1
  • 35
    • 0000565347 scopus 로고
    • The metric theory of interval exchange transformations I: Generic spectral properties
    • W. A. Veech, The metric theory of interval exchange transformations I: Generic spectral properties, Amer. J. Math. 106 (1984), 1331-1359.
    • (1984) Amer. J. Math. , vol.106 , pp. 1331-1359
    • Veech, W.A.1
  • 36
    • 0000565348 scopus 로고
    • The metric theory of interval exchange transformations II: Approximation by primitive interval exchanges
    • W. A. Veech, The metric theory of interval exchange transformations II: Approximation by primitive interval exchanges. Amer. J. Math. 106 (1984), 1361-1387.
    • (1984) Amer. J. Math. , vol.106 , pp. 1361-1387
    • Veech, W.A.1
  • 37
    • 0000565347 scopus 로고
    • The metric theory of interval exchange transformations III: The Sah-Arnoux-Fathi invariant
    • W. A. Veech, The metric theory of interval exchange transformations III: The Sah-Arnoux-Fathi invariant. Amer. J. Math. 106 (1984), 1389-1422.
    • (1984) Amer. J. Math. , vol.106 , pp. 1389-1422
    • Veech, W.A.1


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