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July  2016, 36(7): 3511-3518. doi: 10.3934/dcds.2016.36.3511

Anomalous cw-expansive surface homeomorphisms

Alfonso Artigue 1,

1. 

Departamento de Matemática y Estadística del Litoral, Universidad de la República, Gral. Rivera 1350, Salto

Received  June 2015 Revised  January 2016 Published  March 2016

We prove that the genus two surface admits a cw-expansive homeomorphism with a fixed point whose local stable set is not locally connected.
Keywords: continuum theory., Continuum-wise expansive homeomorphism, derived from Anosov diffeomorphism, surface homeomorphism.
Mathematics Subject Classification: Primary: 37E30; Secondary: 37B4.
Citation: Alfonso Artigue. Anomalous cw-expansive surface homeomorphisms. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3511-3518. doi: 10.3934/dcds.2016.36.3511
References:
[1]

A. Artigue, Robustly N-expansive surface diffeomorphisms,, Disc. and Cont. Dyn. Sys., 36 (2016), 2367. doi: 10.3934/dcds.2016.36.2367. Google Scholar

[2]

A. Artigue, M. J. Pacífico and J. L. Vieitez, N-expansive homeomorphisms on surfaces,, 2013, (). Google Scholar

[3]

A. Artigue and D. Carrasco, A note on measure-expansive diffeomorphisms,, J. Math. Anal. Appl., 428 (2015), 713. doi: 10.1016/j.jmaa.2015.02.052. Google Scholar

[4]

G. Hector and U. Hirsch, Introduction to the Geometry of Foliations Part B,, 2nd ed. Friedr. Vieweg & Sohn, (1987). doi: 10.1007/978-3-322-90161-3. Google Scholar

[5]

K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov,, Osaka J. Math., 27 (1990), 117. Google Scholar

[6]

H. Kato, Continuum-wise expansive homeomorphisms,, Canad. J. Math., 45 (1993), 576. doi: 10.4153/CJM-1993-030-4. Google Scholar

[7]

J. Lewowicz, Expansive homeomorphisms of surfaces,, Bol. Soc. Bras. Mat., 20 (1989), 113. doi: 10.1007/BF02585472. Google Scholar

[8]

C. A. Morales, A generalization of expansivity,, Disc. and Cont. Dyn. Sys., 32 (2012), 293. doi: 10.3934/dcds.2012.32.293. Google Scholar

[9]

C. A. Morales and V. F. Sirvent, Expansive Measures,, 29 Colóquio Brasileiro de Matemática, (2013). Google Scholar

[10]

M. J. Pacifico, E. R. Pujals and J. L. Vieitez, Robustly expansive homoclinic classes,, Ergodic Theory Dynam. Systems, 25 (2005), 271. doi: 10.1017/S0143385704000203. Google Scholar

[11]

M. J. Pacifico and J. L. Vieitez, Entropy expansiveness and domination for surface diffeomorphisms,, Rev. Mat. Complut., 21 (2008), 293. doi: 10.5209/rev_REMA.2008.v21.n2.16370. Google Scholar

[12]

J. H. Roberts and N. E. Steenrod, Monotone transformations of two-dimensional manifolds,, Annals of Mathematics, 39 (1938), 851. doi: 10.2307/1968468. Google Scholar

[13]

C. Robinson, Dynamical Systems,, CRC Press, (1995). Google Scholar

show all references

References:
[1]

A. Artigue, Robustly N-expansive surface diffeomorphisms,, Disc. and Cont. Dyn. Sys., 36 (2016), 2367. doi: 10.3934/dcds.2016.36.2367. Google Scholar

[2]

A. Artigue, M. J. Pacífico and J. L. Vieitez, N-expansive homeomorphisms on surfaces,, 2013, (). Google Scholar

[3]

A. Artigue and D. Carrasco, A note on measure-expansive diffeomorphisms,, J. Math. Anal. Appl., 428 (2015), 713. doi: 10.1016/j.jmaa.2015.02.052. Google Scholar

[4]

G. Hector and U. Hirsch, Introduction to the Geometry of Foliations Part B,, 2nd ed. Friedr. Vieweg & Sohn, (1987). doi: 10.1007/978-3-322-90161-3. Google Scholar

[5]

K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov,, Osaka J. Math., 27 (1990), 117. Google Scholar

[6]

H. Kato, Continuum-wise expansive homeomorphisms,, Canad. J. Math., 45 (1993), 576. doi: 10.4153/CJM-1993-030-4. Google Scholar

[7]

J. Lewowicz, Expansive homeomorphisms of surfaces,, Bol. Soc. Bras. Mat., 20 (1989), 113. doi: 10.1007/BF02585472. Google Scholar

[8]

C. A. Morales, A generalization of expansivity,, Disc. and Cont. Dyn. Sys., 32 (2012), 293. doi: 10.3934/dcds.2012.32.293. Google Scholar

[9]

C. A. Morales and V. F. Sirvent, Expansive Measures,, 29 Colóquio Brasileiro de Matemática, (2013). Google Scholar

[10]

M. J. Pacifico, E. R. Pujals and J. L. Vieitez, Robustly expansive homoclinic classes,, Ergodic Theory Dynam. Systems, 25 (2005), 271. doi: 10.1017/S0143385704000203. Google Scholar

[11]

M. J. Pacifico and J. L. Vieitez, Entropy expansiveness and domination for surface diffeomorphisms,, Rev. Mat. Complut., 21 (2008), 293. doi: 10.5209/rev_REMA.2008.v21.n2.16370. Google Scholar

[12]

J. H. Roberts and N. E. Steenrod, Monotone transformations of two-dimensional manifolds,, Annals of Mathematics, 39 (1938), 851. doi: 10.2307/1968468. Google Scholar

[13]

C. Robinson, Dynamical Systems,, CRC Press, (1995). Google Scholar

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