American Institute of Mathematical Sciences

Advanced
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, 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), 2367-2376. 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), 713-716. 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), 117-162.  Google Scholar

[6]

H. Kato, Continuum-wise expansive homeomorphisms, Canad. J. Math., 45 (1993), 576-598. doi: 10.4153/CJM-1993-030-4.  Google Scholar

[7]

J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Bras. Mat., 20 (1989), 113-133. doi: 10.1007/BF02585472.  Google Scholar

[8]

C. A. Morales, A generalization of expansivity, Disc. and Cont. Dyn. Sys., 32 (2012), 293-301. 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), 271-300. 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), 293-317. 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), 851-862. 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), 2367-2376. 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), 713-716. 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), 117-162.  Google Scholar

[6]

H. Kato, Continuum-wise expansive homeomorphisms, Canad. J. Math., 45 (1993), 576-598. doi: 10.4153/CJM-1993-030-4.  Google Scholar

[7]

J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Bras. Mat., 20 (1989), 113-133. doi: 10.1007/BF02585472.  Google Scholar

[8]

C. A. Morales, A generalization of expansivity, Disc. and Cont. Dyn. Sys., 32 (2012), 293-301. 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), 271-300. 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), 293-317. 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), 851-862. doi: 10.2307/1968468.  Google Scholar

[13]

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

[1]

Phoebus Rosakis. Continuum surface energy from a lattice model. Networks & Heterogeneous Media, 2014, 9 (3) : 453-476. doi: 10.3934/nhm.2014.9.453
[2]

Weinan E, Jianfeng Lu. Mathematical theory of solids: From quantum mechanics to continuum models. Discrete & Continuous Dynamical Systems, 2014, 34 (12) : 5085-5097. doi: 10.3934/dcds.2014.34.5085
[3]

Jan J. Dijkstra and Jan van Mill. Homeomorphism groups of manifolds and Erdos space. Electronic Research Announcements, 2004, 10: 29-38.

[4]

Christian Bonatti, Nancy Guelman. Axiom A diffeomorphisms derived from Anosov flows. Journal of Modern Dynamics, 2010, 4 (1) : 1-63. doi: 10.3934/jmd.2010.4.1
[5]

Konstantinos Drakakis, Scott Rickard. On the generalization of the Costas property in the continuum. Advances in Mathematics of Communications, 2008, 2 (2) : 113-130. doi: 10.3934/amc.2008.2.113
[6]

Steffen Klassert, Daniel Lenz, Peter Stollmann. Delone measures of finite local complexity and applications to spectral theory of one-dimensional continuum models of quasicrystals. Discrete & Continuous Dynamical Systems, 2011, 29 (4) : 1553-1571. doi: 10.3934/dcds.2011.29.1553
[7]

Christian Bonatti, Stanislav Minkov, Alexey Okunev, Ivan Shilin. Anosov diffeomorphism with a horseshoe that attracts almost any point. Discrete & Continuous Dynamical Systems, 2020, 40 (1) : 441-465. doi: 10.3934/dcds.2020017
[8]

Dmitri Finkelshtein, Yuri Kondratiev, Yuri Kozitsky. Glauber dynamics in continuum: A constructive approach to evolution of states. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 1431-1450. doi: 10.3934/dcds.2013.33.1431
[9]

Paolo Podio-Guidugli. On the modeling of transport phenomena in continuum and statistical mechanics. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1393-1411. doi: 10.3934/dcdss.2017074
[10]

Piotr Gwiazda, Piotr Minakowski, Agnieszka Świerczewska-Gwiazda. On the anisotropic Orlicz spaces applied in the problems of continuum mechanics. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1291-1306. doi: 10.3934/dcdss.2013.6.1291
[11]

Pranay Goel, James Sneyd. Gap junctions and excitation patterns in continuum models of islets. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1969-1990. doi: 10.3934/dcdsb.2012.17.1969
[12]

Gilles Pijaudier-Cabot, David Grégoire. A review of non local continuum damage: Modelling of failure?. Networks & Heterogeneous Media, 2014, 9 (4) : 575-597. doi: 10.3934/nhm.2014.9.575
[13]

Lijian Jiang, Yalchin Efendiev, Victor Ginting. Multiscale methods for parabolic equations with continuum spatial scales. Discrete & Continuous Dynamical Systems - B, 2007, 8 (4) : 833-859. doi: 10.3934/dcdsb.2007.8.833
[14]

Marek Fila, Juan-Luis Vázquez, Michael Winkler. A continuum of extinction rates for the fast diffusion equation. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1129-1147. doi: 10.3934/cpaa.2011.10.1129
[15]

Gabriella Bretti, Ciro D’Apice, Rosanna Manzo, Benedetto Piccoli. A continuum-discrete model for supply chains dynamics. Networks & Heterogeneous Media, 2007, 2 (4) : 661-694. doi: 10.3934/nhm.2007.2.661
[16]

Franco Cardin, Alberto Lovison. Finite mechanical proxies for a class of reducible continuum systems. Networks & Heterogeneous Media, 2014, 9 (3) : 417-432. doi: 10.3934/nhm.2014.9.417
[17]

G. Idone, A. Maugeri. Variational inequalities and a transport planning for an elastic and continuum model. Journal of Industrial & Management Optimization, 2005, 1 (1) : 81-86. doi: 10.3934/jimo.2005.1.81
[18]

Alfonso Artigue. Robustly N-expansive surface diffeomorphisms. Discrete & Continuous Dynamical Systems, 2016, 36 (5) : 2367-2376. doi: 10.3934/dcds.2016.36.2367
[19]

Artur O. Lopes, Vladimir A. Rosas, Rafael O. Ruggiero. Cohomology and subcohomology problems for expansive, non Anosov geodesic flows. Discrete & Continuous Dynamical Systems, 2007, 17 (2) : 403-422. doi: 10.3934/dcds.2007.17.403
[20]

Yuri Kozitsky, Krzysztof Pilorz. Random jumps and coalescence in the continuum: Evolution of states of an infinite particle system. Discrete & Continuous Dynamical Systems, 2020, 40 (2) : 725-752. doi: 10.3934/dcds.2020059

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (146)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy