The minimal entropy problem for 3-manifolds with zero simplicial volume

Anderson, James W. ; Paternain, Gabriel P.

Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 63-79.

MR Zbl

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     author = {Anderson, James W. and Paternain, Gabriel P.},
     title = {The minimal entropy problem for 3-manifolds with zero simplicial volume},
     booktitle = {Geometric methods in dynamics (I) : Volume in honor of Jacob Palis},
     editor = {de Melo, Wellington and Viana, Marcelo and Yoccoz, Jean-Christophe},
     series = {Ast\'erisque},
     pages = {63--79},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {286},
     year = {2003},
     mrnumber = {2052297},
     zbl = {1056.53054},
     language = {en},
     url = {http://www.numdam.org/item/AST_2003__286__63_0/}
}

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Anderson, James W.; Paternain, Gabriel P. The minimal entropy problem for 3-manifolds with zero simplicial volume, dans Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 63-79. http://www.numdam.org/item/AST_2003__286__63_0/

Bibliographie
Cité par

[1] G. Besson, G. Courtois, S. Gallot, 'Entropies et rigidités des espaces localement symétriques de courbure strictement négative'. Geom. Funct. Anal. 5 (1995) 731-799. | DOI | EuDML | MR | Zbl

[2] F. Bonahon, 'Geometric structures on $3$ -manifolds', Handbook of Geometric Topology, edited by R. Daverman and R. Sher, North-Holland, Amsterdam, 2002, 93-164. | MR | Zbl

[3] J. Cheeger, M. Gromov, 'Collapsing Riemannian manifolds while keeping the curvature bounded. I', J. Diff. Geometry 23 (1986) 309-346. | DOI | MR | Zbl

[4] C. Connell and B. Farb. 'Minimal entropy rigidity for lattices in products of rank one symmetric spaces', to appear in Comm. Anal. Geom. | MR | Zbl

[5] E. I. Dinaburg, 'On the relations among various entropy characteristics of dynamical systems', Math. USSR Izv. 5 (1971) 337 378. | DOI | Zbl

[6] B. Evans, L. Moser, 'Solvable fundamental groups of compact $3$ -manifolds', Trans. Amer. Math. Soc. 168 (1972), 189-210. | MR | Zbl

[7] M. Gromov. 'Volume and bounded cohomology', Publ. Math. I.H.E.S. 56 (1982) 5-99. | EuDML | Numdam | MR | Zbl

[8] J. Hempel. $3$ -manifolds, Annals of Mathematics Studies 86, Princeton University Press, 1976. | MR | Zbl

[9] W. Jaco and P. B. Shalen, Seifert fibered spaces in $3$ -manifolds, Memoirs of the AMS 220, American Mathematical Society, Providence, 1979. | MR | Zbl

[10] K. Johannson, 'Homotopy equivalences of $3$ -manifolds with boundary', Lecture Notes in Mathematics 761, Springer-Verlag, 1979. | MR | Zbl

[11] A. Katok, 'Entropy and closed geodesics', Ergod. Th. and Dynam. Syst. 2 (1982) 339-369. | DOI | MR | Zbl

[12] H. Kneser, 'Geschlossene Flächen in dreidimensionale Mannigflatigkeiten', Jahresber. Deutsch. Mat. Verein 38 (1929) 248-260. | EuDML | JFM

[13] A. Manning, 'Topological entropy for geodesic flows', Ann. Math. 110 (1979), 567-573. | DOI | MR | Zbl

[14] R. Mañé, 'On the topological entropy of geodesic flows', J. Differential Geom. 45 (1997) 74-93. | DOI | MR | Zbl

[15] J. Milnor, 'A note on curvature and fundamental group', J. Diff. Geometry 2 (1968) 1-7. | DOI | MR | Zbl

[16] J. Milnor, 'A unique factorisation theorem for $3$ -manifolds', Amer. J. Math. 84 (1962) 1-7. | DOI | MR | Zbl

[17] J. Morgan, 'On Thurston's uniformization theorem for $3$ -dimensional manifolds', in The Smith conjecture, ed. by H. Bass and J. Morgan, Academic Press, 1984, 37-126. | MR | Zbl

[18] G. Mostow, 'Strong rigidity of locally symmetric spaces'. Annals of Mathematics Studies 78, Princeton University Press, 1973. | MR | Zbl

[19] J.-P. Otal, 'Thurston's hyperbolization of Haken manifolds', in Surveys in differential geometry III, ed. by C.-C. Hsiung and S.-T. Yau, International Press, Boston, 1998, 77-194. | MR | Zbl

[20] G. P. Paternain, Geodesic Flows, Progress in Mathematics 180, Birkhäuser, 1999. | MR | Zbl

[21] G. P. Paternain, J. Petean, Minimal entropy and collapsing with curvature bounded from below, Invent. Math. 151 (2003) 415-450. | DOI | MR | Zbl

[22] J. F. Plante, W. P. Thurston, 'Anosov flows and the fundamental group'. Topology 11 (1972) 147-150. | DOI | MR | Zbl

[23] X. Rong, 'The limiting eta invariants of collapsed three-manifolds', J. Diff. Geometry 37 (1993) 535-568. | DOI | MR | Zbl

[24] D. Ruelle, 'An inequality for the entropy of differentiable maps', Bol. Soc. Brasil. Mat., 9 (1978) 83-87. | DOI | MR | Zbl

[25] G. P. Scott, 'A new proof of the annulus and torus theorems'. Amer. J. Math. 102 (1980) 241-277. | DOI | MR | Zbl

[26] G. P. Scott, 'The geometries of $3$ -manifolds', Bull. Lond. Math. Soc. 15 (1983) 401-487. | DOI | MR | Zbl

[27] G. P. Scott, Math. Review 96f:57011, 1996.

[28] T. Soma, 'The Gromov invariant for links'. Invent. Math. 64 (1981) 445-454. | DOI | EuDML | MR | Zbl

[29] W. P. Thurston, 'The geometry and topology of three-manifolds', electronic version 1.0- October 1997.

[30] W. P. Thurston, 'Three dimensional manifolds, Kleinian groups, and hyperbolic geometry', Bull. Amer. Math. Soc. 6 (1982), 357-381. | DOI | MR | Zbl