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Expansion growth, entropy and invariant measures of distal groups and pseudogroups of homeo- and diffeomorphisms
1. | Katedra Geometrii, Wydział Matematyki i Informatyki, Uniwersytet Łódzki, Łódź, Poland |
References:
[1] |
J. Alvarez Lopez and A. Candel, Equicontinuous foliated spaces, Math. Z., 263 (2009), 725-774.
doi: 10.1007/s00209-008-0432-4. |
[2] |
M. Badura, Prescribing growth type of complete Riemannian manifolds of bounded geometry, Ann. Polon. Math., 75 (2000), 167-175. |
[3] |
S. Banach, On Haar measure, Uspekhi Mat. Nauk, 2 (1936), 161-167. |
[4] |
A. Biś and P. Walczak, Entropy of distal groups, pseudogroups and laminations, Ann. Polon. Math., 100 (2011), 45-54.
doi: 10.4064/ap100-1-5. |
[5] |
A. Candel and L. Conlon, "Foliations I," Amer. Math. Soc., Providence, 2000. |
[6] |
S. Egashira, Expansion growth of foliations, Ann. Fac. Sci. Toulouse, 2 (1993), 15-52.
doi: 10.5802/afst.756. |
[7] |
R. Ellis, Distal transformation groups, Pacific J. Math., 24 (1957), 401-405.
doi: 10.2140/pjm.1958.8.401. |
[8] |
H. Furstenberg, The structure of distal flows, Amer. J. Math., 85 (1963), 477-515.
doi: 10.2307/2373137. |
[9] |
E. Ghys, R. Langevin and P. Walczak, Entropie géométrique des feuilletages, Acta Math., 160 (1988), 105-142.
doi: 10.1007/BF02392274. |
[10] |
A. Haefliger, Foliations and compactly generated pseudogroups, in "Foliations: Geometry and Dynamics," Proc. of the Conf., Warsaw (2000), World Sci. Publ., Singapore (2002), 275-295.
doi: 10.1142/9789812778246_0013. |
[11] |
S. Matsumoto, The unique ergodicity of equicontinuous laminations, Hokkaido Math. J., 39 (2010), 389-403. |
[12] |
W. Parry, Zero entropy of distal and related transformations, in "Topological Dynamics: An International Symposium" (eds. J. Auslander and W. H. Gottschalk), W. A. Benjamin, New York (1968), pp. 383-389. |
[13] |
M. Rees, "On the Structure of Minimal Distal Transformation Groups with Topological Manifolds as Phase Spaces," thesis, University of Warwick, 1977. |
[14] |
W. Rudin, "Real and Complex Analysis," McGraw-Hill, New York, London etc., 1966. |
[15] |
S. Saks, "Monografie Matematyczne," Theory of the Integral, 7, Warszawa - Lwów, 1937. |
[16] |
P. Walczak, "Dynamics of Foliations, Groups and Pseudogroups," Monografie Matematyczne, 64, Birkhäuser, Basel, 2004,
doi: 10.1007/978-3-0348-7887-6. |
[17] |
A. Weil, "L'intégration dans les Groupes Topologiques et ses Applications," (French) [This book has been republished by the author at Princeton, N. J., 1941.], Actual. Sci. Ind., 869, Hermann et Cie, Paris, 1940. |
show all references
References:
[1] |
J. Alvarez Lopez and A. Candel, Equicontinuous foliated spaces, Math. Z., 263 (2009), 725-774.
doi: 10.1007/s00209-008-0432-4. |
[2] |
M. Badura, Prescribing growth type of complete Riemannian manifolds of bounded geometry, Ann. Polon. Math., 75 (2000), 167-175. |
[3] |
S. Banach, On Haar measure, Uspekhi Mat. Nauk, 2 (1936), 161-167. |
[4] |
A. Biś and P. Walczak, Entropy of distal groups, pseudogroups and laminations, Ann. Polon. Math., 100 (2011), 45-54.
doi: 10.4064/ap100-1-5. |
[5] |
A. Candel and L. Conlon, "Foliations I," Amer. Math. Soc., Providence, 2000. |
[6] |
S. Egashira, Expansion growth of foliations, Ann. Fac. Sci. Toulouse, 2 (1993), 15-52.
doi: 10.5802/afst.756. |
[7] |
R. Ellis, Distal transformation groups, Pacific J. Math., 24 (1957), 401-405.
doi: 10.2140/pjm.1958.8.401. |
[8] |
H. Furstenberg, The structure of distal flows, Amer. J. Math., 85 (1963), 477-515.
doi: 10.2307/2373137. |
[9] |
E. Ghys, R. Langevin and P. Walczak, Entropie géométrique des feuilletages, Acta Math., 160 (1988), 105-142.
doi: 10.1007/BF02392274. |
[10] |
A. Haefliger, Foliations and compactly generated pseudogroups, in "Foliations: Geometry and Dynamics," Proc. of the Conf., Warsaw (2000), World Sci. Publ., Singapore (2002), 275-295.
doi: 10.1142/9789812778246_0013. |
[11] |
S. Matsumoto, The unique ergodicity of equicontinuous laminations, Hokkaido Math. J., 39 (2010), 389-403. |
[12] |
W. Parry, Zero entropy of distal and related transformations, in "Topological Dynamics: An International Symposium" (eds. J. Auslander and W. H. Gottschalk), W. A. Benjamin, New York (1968), pp. 383-389. |
[13] |
M. Rees, "On the Structure of Minimal Distal Transformation Groups with Topological Manifolds as Phase Spaces," thesis, University of Warwick, 1977. |
[14] |
W. Rudin, "Real and Complex Analysis," McGraw-Hill, New York, London etc., 1966. |
[15] |
S. Saks, "Monografie Matematyczne," Theory of the Integral, 7, Warszawa - Lwów, 1937. |
[16] |
P. Walczak, "Dynamics of Foliations, Groups and Pseudogroups," Monografie Matematyczne, 64, Birkhäuser, Basel, 2004,
doi: 10.1007/978-3-0348-7887-6. |
[17] |
A. Weil, "L'intégration dans les Groupes Topologiques et ses Applications," (French) [This book has been republished by the author at Princeton, N. J., 1941.], Actual. Sci. Ind., 869, Hermann et Cie, Paris, 1940. |
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