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Actions of solvable Baumslag-Solitar groups on surfaces with (pseudo)-Anosov elements
Lipschitz perturbations of expansive systems
1. | Departamento de Matemática y Estadística del Litoral, Universidad de la República, Gral. Rivera 1350, Salto |
References:
[1] |
N. H. Bingham and A. J. Ostaszewski, Normed versus topological groups: Dichotomy and duality, Dissertationes Mathematicae, 472 (2010), 138pp.
doi: 10.4064/dm472-0-1. |
[2] |
A. Fathi, Expansiveness, hyperbolicity and Hausdorff dimension, Commun. Math. Phys., 126 (1989), 249-262.
doi: 10.1007/BF02125125. |
[3] |
K. Fukui and T. Nakamura, A topological property of Lipschitz mappings, Topology Appl., 148 (2005), 143-152.
doi: 10.1016/j.topol.2004.08.005. |
[4] |
J. Harrison, Unsmoothable diffeomorphisms on higher dimensional manifolds, Proc. Amer. Math. Soc., 73 (1979), 249-255.
doi: 10.1090/S0002-9939-1979-0516473-9. |
[5] |
K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov, Osaka J. Math., 27 (1990), 117-162. |
[6] |
E. Jeandenans, Difféomorphismes Hyperboliques Des Surfaces Et Combinatoire Des Partitions De Markov, Thesis, 1996. |
[7] |
J. Lewowicz, Lyapunov functions and topological stability, J. Diff. Eq., 38 (1980), 192-209.
doi: 10.1016/0022-0396(80)90004-2. |
[8] |
J. Lewowicz, Persistence in expansive systems, Erg. Th. & Dyn. Sys., 3 (1983), 567-578.
doi: 10.1017/S0143385700002157. |
[9] |
J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Brasil. Mat. (N.S.), 20 (1989), 113-133.
doi: 10.1007/BF02585472. |
[10] |
R. Mañé, Expansive diffeomorphisms, Lecture Notes in Math., Springer, Berlin, 468 (1975), 162-174. |
[11] |
H. Masur and J. Smillie, Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms, Comment. Math. Helvetici, 68 (1993), 289-307.
doi: 10.1007/BF02565820. |
[12] |
S. Yu. Pilyugin, A. A. Rodionova and K. Sakai, Orbital and weak shadowing properties, Discrete and continuous dynamical systems, 9 (2003), 287-308.
doi: 10.3934/dcds.2003.9.287. |
[13] |
S. Yu. Pilyugin and S. B. Tikhomirov, Lipschitz shadowing implies structural stability, Nonlinearity, 23 (2010), 2509-2515.
doi: 10.1088/0951-7715/23/10/009. |
[14] |
C. Robinson, Dynamical Systems, CRC Press, $2^{nd}$ edition, 1999. |
[15] |
K. Sakai and R. Y. Wong, Conjugating homeomorphisms to uniform homeomorphisms, Trans. Amer. Math. Soc., 311 (1989), 337-356.
doi: 10.1090/S0002-9947-1989-0974780-0. |
[16] |
K. Takaki, Lipeomorphisms close to an Anosov diffeomorphism, Nagoya Math. J., 53 (1974), 71-82. |
[17] |
P. Walters, On the pseudo orbit tracing property and its relationship to stability, Lecture Notes in Math., Springer, 668 (1978), 231-244. |
[18] |
F. W. Wilson, Pasting diffeomorphisms of $R^n$, Illinois J. Math., 16 (1972), 222-233. |
show all references
References:
[1] |
N. H. Bingham and A. J. Ostaszewski, Normed versus topological groups: Dichotomy and duality, Dissertationes Mathematicae, 472 (2010), 138pp.
doi: 10.4064/dm472-0-1. |
[2] |
A. Fathi, Expansiveness, hyperbolicity and Hausdorff dimension, Commun. Math. Phys., 126 (1989), 249-262.
doi: 10.1007/BF02125125. |
[3] |
K. Fukui and T. Nakamura, A topological property of Lipschitz mappings, Topology Appl., 148 (2005), 143-152.
doi: 10.1016/j.topol.2004.08.005. |
[4] |
J. Harrison, Unsmoothable diffeomorphisms on higher dimensional manifolds, Proc. Amer. Math. Soc., 73 (1979), 249-255.
doi: 10.1090/S0002-9939-1979-0516473-9. |
[5] |
K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov, Osaka J. Math., 27 (1990), 117-162. |
[6] |
E. Jeandenans, Difféomorphismes Hyperboliques Des Surfaces Et Combinatoire Des Partitions De Markov, Thesis, 1996. |
[7] |
J. Lewowicz, Lyapunov functions and topological stability, J. Diff. Eq., 38 (1980), 192-209.
doi: 10.1016/0022-0396(80)90004-2. |
[8] |
J. Lewowicz, Persistence in expansive systems, Erg. Th. & Dyn. Sys., 3 (1983), 567-578.
doi: 10.1017/S0143385700002157. |
[9] |
J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Brasil. Mat. (N.S.), 20 (1989), 113-133.
doi: 10.1007/BF02585472. |
[10] |
R. Mañé, Expansive diffeomorphisms, Lecture Notes in Math., Springer, Berlin, 468 (1975), 162-174. |
[11] |
H. Masur and J. Smillie, Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms, Comment. Math. Helvetici, 68 (1993), 289-307.
doi: 10.1007/BF02565820. |
[12] |
S. Yu. Pilyugin, A. A. Rodionova and K. Sakai, Orbital and weak shadowing properties, Discrete and continuous dynamical systems, 9 (2003), 287-308.
doi: 10.3934/dcds.2003.9.287. |
[13] |
S. Yu. Pilyugin and S. B. Tikhomirov, Lipschitz shadowing implies structural stability, Nonlinearity, 23 (2010), 2509-2515.
doi: 10.1088/0951-7715/23/10/009. |
[14] |
C. Robinson, Dynamical Systems, CRC Press, $2^{nd}$ edition, 1999. |
[15] |
K. Sakai and R. Y. Wong, Conjugating homeomorphisms to uniform homeomorphisms, Trans. Amer. Math. Soc., 311 (1989), 337-356.
doi: 10.1090/S0002-9947-1989-0974780-0. |
[16] |
K. Takaki, Lipeomorphisms close to an Anosov diffeomorphism, Nagoya Math. J., 53 (1974), 71-82. |
[17] |
P. Walters, On the pseudo orbit tracing property and its relationship to stability, Lecture Notes in Math., Springer, 668 (1978), 231-244. |
[18] |
F. W. Wilson, Pasting diffeomorphisms of $R^n$, Illinois J. Math., 16 (1972), 222-233. |
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