메뉴 건너뛰기




Volumn 146, Issue 2, 1997, Pages 295-344

Solutions of the cohomological equation for area-preserving flows on compact surfaces of higher genus

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0031513831     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/2952464     Document Type: Article
Times cited : (87)

References (47)
  • 2
    • 0010935594 scopus 로고
    • On some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems)
    • Russian
    • S. H. ARANSON and V. Z. GRINES, On some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems), Mat. Sb.90(132)(1973), 372-402 (Russian). Transl. in Math. USSR Sb. 19(1973), 365-393.
    • (1973) Mat. Sb. , vol.90 , Issue.132 , pp. 372-402
    • Aranson, S.H.1    Grines, V.Z.2
  • 3
    • 0000400428 scopus 로고
    • Transl.
    • S. H. ARANSON and V. Z. GRINES, On some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems), Mat. Sb.90(132)(1973), 372-402 (Russian). Transl. in Math. USSR Sb. 19(1973), 365-393.
    • (1973) Math. USSR Sb. , vol.19 , pp. 365-393
  • 4
    • 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
  • 5
    • 84974220147 scopus 로고
    • Rank two interval exchange tranformations
    • _, Rank two interval exchange tranformations, Ergod. Th. Dynam. Sys. 8(1988), 379-394.
    • (1988) Ergod. Th. Dynam. Sys. , vol.8 , pp. 379-394
  • 7
    • 0001679198 scopus 로고
    • On the spectral geometry of spaces with cone-like singularities
    • J. CHEEGER, On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci. U.S.A. 76(1979), 2103-2106.
    • (1979) Proc. Nat. Acad. Sci. U.S.A. , vol.76 , pp. 2103-2106
    • Cheeger, J.1
  • 8
    • 0001976993 scopus 로고
    • On the Hodge theory of riemannian pseudomanifolds
    • Amer. Math. Soc., Providence, RI
    • _, On the Hodge theory of riemannian pseudomanifolds, in Proc. Sympos. Pure Math. 36 (1980), 1946, Amer. Math. Soc., Providence, RI.
    • (1980) Proc. Sympos. Pure Math. , vol.36 , pp. 1946
  • 9
    • 84972545480 scopus 로고
    • Spectral geometry of singular Riemannian spaces
    • _, Spectral geometry of singular Riemannian spaces, J. Differ. Geom. 18 (1983), 575-657.
    • (1983) J. Differ. Geom. , vol.18 , pp. 575-657
  • 10
    • 84990581570 scopus 로고
    • On the diffraction of waves by conical singularities, I & II
    • J. CHEEGER and M. TAYLOR, On the diffraction of waves by conical singularities, I & II, Comm. Pure Appl. Math. 35(1982), 275-331 and 487-529.
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 275-331
    • Cheeger, J.1    Taylor, M.2
  • 11
    • 0011514669 scopus 로고
    • Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties
    • P. COLLET, H. EPSTEIN, and G. GALLAVOTTI, Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties, Comm. Math. Phys. 95 (1984), 61-112.
    • (1984) Comm. Math. Phys. , vol.95 , pp. 61-112
    • Collet, P.1    Epstein, H.2    Gallavotti, G.3
  • 13
    • 0002750126 scopus 로고
    • Curves on 2-manifolds and isotopies
    • D. B. A. EPSTEIN, Curves on 2-manifolds and isotopies, Acta Math. 115(1966), 83-107.
    • (1966) Acta Math. , vol.115 , pp. 83-107
    • Epstein, D.B.A.1
  • 14
    • 0004152420 scopus 로고
    • Springer-Verlag, New York, (second edition)
    • H. M. FARKAS and I. KRA, Riemann Surfaces, Springer-Verlag, New York, 1992 (second edition).
    • (1992) Riemann Surfaces
    • Farkas, H.M.1    Kra, I.2
  • 16
    • 0001737037 scopus 로고
    • Séries trigonométriques; et séries de Taylor
    • P. FATOU, Séries trigonométriques; et séries de Taylor, Acta Math. 30(1906), 335-400.
    • (1906) Acta Math. , vol.30 , pp. 335-400
    • Fatou, P.1
  • 17
    • 0001468554 scopus 로고
    • A special Stokes's theorem for complete Riemannian manifolds
    • M. P. GAFFNEY, A special Stokes's theorem for complete Riemannian manifolds, Ann. of Math. 60(1954), 140-145.
    • (1954) Ann. of Math. , vol.60 , pp. 140-145
    • Gaffney, M.P.1
  • 18
    • 51249192662 scopus 로고
    • A maximal theorem with function-theoretic applications
    • G. H. HARDY and J. E. LITTLEWOOD, A maximal theorem with function-theoretic applications, Acta Math. 54(1930), 81-116.
    • (1930) Acta Math. , vol.54 , pp. 81-116
    • Hardy, G.H.1    Littlewood, J.E.2
  • 19
    • 0001096985 scopus 로고
    • Quadratic differentials and foliations
    • J. HUBBARD and H. MASUR, Quadratic differentials and foliations, Acta Math. 142(1979), 221-274.
    • (1979) Acta Math. , vol.142 , pp. 221-274
    • Hubbard, J.1    Masur, H.2
  • 20
    • 0009887437 scopus 로고
    • Invariant measures of flows on oriented surfaces
    • A. KATOK, Invariant measures of flows on oriented surfaces, Dokl. Naukl. SSR 211(1973). English transl. in Sov. Math. Dokl. 14(1973), 1104-1108.
    • (1973) Dokl. Naukl. SSR , vol.211
    • Katok, A.1
  • 21
    • 0010950986 scopus 로고
    • English transl.
    • A. KATOK, Invariant measures of flows on oriented surfaces, Dokl. Naukl. SSR 211(1973). English transl. in Sov. Math. Dokl. 14(1973), 1104-1108.
    • (1973) Sov. Math. Dokl. , vol.14 , pp. 1104-1108
  • 23
    • 0002772850 scopus 로고
    • Interval exchange transformations
    • M. KEANE, Interval exchange transformations, Math. Z. 141(1975), 25-31.
    • (1975) Math. Z. , vol.141 , pp. 25-31
    • Keane, M.1
  • 24
    • 0000511668 scopus 로고
    • Non-ergodic interval exchange transformations
    • _, Non-ergodic interval exchange transformations, Israel J. Math. 2(1977), 188-196.
    • (1977) Israel J. Math. , vol.2 , pp. 188-196
  • 25
    • 84958429324 scopus 로고
    • Simplicial systems for interval exchange maps and measured foliations
    • S. KERCKHOFF, Simplicial systems for interval exchange maps and measured foliations, Ergod. Th. Dynam. Sys. 5(1985), 257-271.
    • (1985) Ergod. Th. Dynam. Sys. , vol.5 , pp. 257-271
    • Kerckhoff, S.1
  • 26
    • 0000923571 scopus 로고
    • Ergodicity of billiard flows and quadratic differentials
    • S. KERCKHOFF, H. MASUR, and J. SMILLIE, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. 124(1986), 293-311.
    • (1986) Ann. of Math. , vol.124 , pp. 293-311
    • Kerckhoff, S.1    Masur, H.2    Smillie, J.3
  • 27
    • 34250466764 scopus 로고
    • Homology properties of Y-systems
    • A. LIVSHITZ, Homology properties of Y-systems, Math. Notes USSR Acad. Sci. 10(1971), 758-763.
    • (1971) Math. Notes USSR Acad. Sci. , vol.10 , pp. 758-763
    • Livshitz, A.1
  • 28
    • 0000174457 scopus 로고
    • Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
    • R. DE LA LLAVE, J. MARKO, and R. MORIYON, Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation, Ann. of Math. 123 (1986), 537-611.
    • (1986) Ann. of Math. , vol.123 , pp. 537-611
    • De La Llave, R.1    Marko, J.2    Moriyon, R.3
  • 29
    • 0002172154 scopus 로고
    • Trajectories on the closed orientable surfaces
    • Russian
    • A. G. MAIER, Trajectories on the closed orientable surfaces, Mat. Sb. 12(54)(1943), 71-84 (Russian).
    • (1943) Mat. Sb. , vol.12 , Issue.54 , pp. 71-84
    • Maier, A.G.1
  • 30
    • 0000742775 scopus 로고
    • Interval exchange transformations and measured foliations
    • H. MASUR, Interval exchange transformations and measured foliations, Ann. of Math. 115(1982), 168-200.
    • (1982) Ann. of Math. , vol.115 , pp. 168-200
    • Masur, H.1
  • 31
    • 0000534712 scopus 로고
    • Hausdorff dimension of sets of nonergodic measured foliations
    • H. MASUR and J. SMILLIE, Hausdorff dimension of sets of nonergodic measured foliations, Ann. of Math. 134(1991), 455-543.
    • (1991) Ann. of Math. , vol.134 , pp. 455-543
    • Masur, H.1    Smillie, J.2
  • 32
    • 0000769597 scopus 로고
    • Analytic vectors
    • E. NELSON, Analytic vectors, Ann. of Math. 70(1959), 572-615.
    • (1959) Ann. of Math. , vol.70 , pp. 572-615
    • Nelson, E.1
  • 33
    • 0003831421 scopus 로고
    • Cambridge Univ. Press, Cambridge, UK
    • K. PETERSEN, Ergodic Theory, Cambridge Univ. Press, Cambridge, UK, 1983.
    • (1983) Ergodic Theory
    • Petersen, K.1
  • 35
    • 0002604975 scopus 로고
    • An alternative approach to the ergodic theory of measured foliations on surfaces
    • M. REES, An alternative approach to the ergodic theory of measured foliations on surfaces, Ergod. Th. Dynam. Sys. 1(1981), 461-488.
    • (1981) Ergod. Th. Dynam. Sys. , vol.1 , pp. 461-488
    • Rees, M.1
  • 36
    • 0002438337 scopus 로고
    • Über die randwerte einer analytischen funktion
    • F. RIESZ, Über die Randwerte einer analytischen Funktion, Math. Z. 18(1923), 87-95.
    • (1923) Math. Z. , vol.18 , pp. 87-95
    • Riesz, F.1
  • 37
    • 0006411015 scopus 로고
    • McGraw-Hill Book Company, New York, (third edition)
    • W. RUDIN, Real & Complex Analysis, McGraw-Hill Book Company, New York, 1987 (third edition).
    • (1987) Real & Complex Analysis
    • Rudin, W.1
  • 38
    • 0040869028 scopus 로고
    • Sur les valeurs limites des fonctions régulières à l'intérieur d'un cercle
    • V. SMIRNOV, Sur les valeurs limites des fonctions régulières à l'intérieur d'un cercle, J. de la Soc. Physico-Mathématique de Leningrad 2(1929), 22-37.
    • (1929) J. de la Soc. Physico-mathématique de Leningrad , vol.2 , pp. 22-37
    • Smirnov, V.1
  • 41
    • 84968476184 scopus 로고
    • On the geometry and dynamics of diffeomorphisms of surfaces
    • W. THURSTON, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. A.M.S. 19(1988), 417-431.
    • (1988) Bull. A.M.S. , vol.19 , pp. 417-431
    • Thurston, W.1
  • 42
    • 51249180903 scopus 로고
    • Interval exchange transformations
    • W. VEECH, Interval exchange transformations, J. Analyse Math. 33(1978), 222-272.
    • (1978) J. Analyse Math. , vol.33 , pp. 222-272
    • Veech, W.1
  • 43
    • 10044293414 scopus 로고
    • Projective swiss cheeses and uniquely ergodic interval exchange transformations
    • _, Projective swiss cheeses and uniquely ergodic interval exchange transformations, Ergod. Th. Dynam. Sys. 1(1981), 113-195.
    • (1981) Ergod. Th. Dynam. Sys. , vol.1 , pp. 113-195
  • 44
    • 0000742776 scopus 로고
    • Gauss measures for transformations on the space of interval exchange maps
    • _, 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
  • 45
    • 84974281172 scopus 로고
    • Boshernitzan's criterion for unique ergodicity of an interval exchange transformation
    • _, Boshernitzan's criterion for unique ergodicity of an interval exchange transformation, Ergod. Th. Dynam. Sys. 7 (1987), 149-153.
    • (1987) Ergod. Th. Dynam. Sys. , vol.7 , pp. 149-153
  • 46
    • 0004021335 scopus 로고
    • Springer-Verlag, New York Berlin, (sixth edition)
    • K. YOSIDA, Functional Analysis, Springer-Verlag, New York Berlin, 1980 (sixth edition).
    • (1980) Functional Analysis
    • Yosida, K.1
  • 47
    • 84953751498 scopus 로고
    • Cambridge Univ. Press, Cambridge, U.K. (reprinted in)
    • A. ZYGMUND, Trigonometric Series, Cambridge Univ. Press, Cambridge, U.K. 1959 (reprinted in 1990).
    • (1959) Trigonometric Series
    • Zygmund, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.