-
Previous Article
Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices
- DCDS Home
- This Issue
-
Next Article
Inertial manifolds for a class of non-autonomous semilinear parabolic equations with finite delay
Expansive flows of surfaces
1. | Departamento de Matemática y Estadística del Litoral, Universidad de la República, Gral. Rivera 1350, Salto, Uruguay |
References:
[1] |
R. Bowen and P. Walters, Expansive one-parameter flows, J. Differential Equations, 12 (1972), 180-193.
doi: 10.1016/0022-0396(72)90013-7. |
[2] |
M. Cobo, C. Gutiérrez and J. Llibre, Flows without wandering points on compact connected surfaces, Trans. Amer. Math. Soc., 362 (2010), 4569-4580.
doi: 10.1090/S0002-9947-10-05113-5. |
[3] |
G. Gal'perin, T. Krüger and S. Troubetzkoy, Local instability of orbits in polygonal and polyhedral billiards, Comm. Math. Phys., 169 (1995), 463-473.
doi: 10.1007/BF02099308. |
[4] |
C. Gutiérrez, Smoothability of Cherry flows on two-manifolds, In Lecture Notes in Math, Springer, Berlin, 1007 (1983), 308-331.
doi: 10.1007/BFb0061422. |
[5] |
C. Gutiérrez, Smoothing continuous flows on two-manifolds and recurrences, Ergodic Theory Dynam. Systems, 6 (1986), 17-44. |
[6] |
P. Hartman, "Ordinary Differential Equations,'' John Wiley & Sons Inc., New York, 1964. |
[7] |
L. F. He and G. Z. Shan, The nonexistence of expansive flow on a compact 2-manifold, Chinese Ann. Math. Ser. B, 12 (1991), 213-218. |
[8] |
K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov, Osaka J. Math, 27 (1990), 117-162. |
[9] |
M. W. Hirsch, "Differential Topology,'' Graduate Texts in Mathematics, No. 33, Springer-Verlag, New York, 1976. |
[10] |
J. F. Jakobsen and W. R. Utz, The non-existence of expansive homeomorphisms on a closed 2-cell, Pacific J. Math, 10 (1960), 1319-1321. |
[11] |
M. Keane, Interval exchange transformations, Math. Z., 141 (1975), 25-31.
doi: 10.1007/BF01236981. |
[12] |
M. Komuro, Expansive properties of Lorenz attractors, The theory of dynamical systems and its applications to nonlinear problems, (Kyoto, 1984), World Sci. Publishing, Singapore, 1984, 4-26. |
[13] |
J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Brasil. Mat. (N.S.), 20 (1989), 113-133.
doi: 10.1007/BF02585472. |
[14] |
N. G. Markley, On the number of recurrent orbit closures, Proc. Amer. Math. Soc., 25 (1970), 413-416.
doi: 10.1090/S0002-9939-1970-0256375-0. |
[15] |
A. Mayer, Trajectories on the closed orientable surfaces, Rec. Math. [Mat. Sbornik] N.S., 12 (1943), 71-84. |
[16] |
M. Oka, Expansiveness of real flows, Tsukuba J. Math, 14 (1990), 1-8. |
[17] |
H. Whitney, Regular families of curves, Ann. of Math, 34 (1933), 244-270.
doi: 10.2307/1968202. |
[18] |
A. N. Zemljakov and A. B. Katok, Topological transitivity of billiards in polygons, Mat. Zametki, 18 (1975), 291-300. |
show all references
References:
[1] |
R. Bowen and P. Walters, Expansive one-parameter flows, J. Differential Equations, 12 (1972), 180-193.
doi: 10.1016/0022-0396(72)90013-7. |
[2] |
M. Cobo, C. Gutiérrez and J. Llibre, Flows without wandering points on compact connected surfaces, Trans. Amer. Math. Soc., 362 (2010), 4569-4580.
doi: 10.1090/S0002-9947-10-05113-5. |
[3] |
G. Gal'perin, T. Krüger and S. Troubetzkoy, Local instability of orbits in polygonal and polyhedral billiards, Comm. Math. Phys., 169 (1995), 463-473.
doi: 10.1007/BF02099308. |
[4] |
C. Gutiérrez, Smoothability of Cherry flows on two-manifolds, In Lecture Notes in Math, Springer, Berlin, 1007 (1983), 308-331.
doi: 10.1007/BFb0061422. |
[5] |
C. Gutiérrez, Smoothing continuous flows on two-manifolds and recurrences, Ergodic Theory Dynam. Systems, 6 (1986), 17-44. |
[6] |
P. Hartman, "Ordinary Differential Equations,'' John Wiley & Sons Inc., New York, 1964. |
[7] |
L. F. He and G. Z. Shan, The nonexistence of expansive flow on a compact 2-manifold, Chinese Ann. Math. Ser. B, 12 (1991), 213-218. |
[8] |
K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov, Osaka J. Math, 27 (1990), 117-162. |
[9] |
M. W. Hirsch, "Differential Topology,'' Graduate Texts in Mathematics, No. 33, Springer-Verlag, New York, 1976. |
[10] |
J. F. Jakobsen and W. R. Utz, The non-existence of expansive homeomorphisms on a closed 2-cell, Pacific J. Math, 10 (1960), 1319-1321. |
[11] |
M. Keane, Interval exchange transformations, Math. Z., 141 (1975), 25-31.
doi: 10.1007/BF01236981. |
[12] |
M. Komuro, Expansive properties of Lorenz attractors, The theory of dynamical systems and its applications to nonlinear problems, (Kyoto, 1984), World Sci. Publishing, Singapore, 1984, 4-26. |
[13] |
J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Brasil. Mat. (N.S.), 20 (1989), 113-133.
doi: 10.1007/BF02585472. |
[14] |
N. G. Markley, On the number of recurrent orbit closures, Proc. Amer. Math. Soc., 25 (1970), 413-416.
doi: 10.1090/S0002-9939-1970-0256375-0. |
[15] |
A. Mayer, Trajectories on the closed orientable surfaces, Rec. Math. [Mat. Sbornik] N.S., 12 (1943), 71-84. |
[16] |
M. Oka, Expansiveness of real flows, Tsukuba J. Math, 14 (1990), 1-8. |
[17] |
H. Whitney, Regular families of curves, Ann. of Math, 34 (1933), 244-270.
doi: 10.2307/1968202. |
[18] |
A. N. Zemljakov and A. B. Katok, Topological transitivity of billiards in polygons, Mat. Zametki, 18 (1975), 291-300. |
[1] |
Giovanni Forni, Carlos Matheus. Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards. Journal of Modern Dynamics, 2014, 8 (3&4) : 271-436. doi: 10.3934/jmd.2014.8.271 |
[2] |
Corinna Ulcigrai. Weak mixing for logarithmic flows over interval exchange transformations. Journal of Modern Dynamics, 2009, 3 (1) : 35-49. doi: 10.3934/jmd.2009.3.35 |
[3] |
Se-Hyun Ku. Expansive flows on uniform spaces. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1585-1598. doi: 10.3934/dcds.2021165 |
[4] |
Alfonso Artigue. Singular cw-expansive flows. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 2945-2956. doi: 10.3934/dcds.2017126 |
[5] |
Mauricio Achigar. Extensions of expansive dynamical systems. Discrete and Continuous Dynamical Systems, 2021, 41 (7) : 3093-3108. doi: 10.3934/dcds.2020399 |
[6] |
Christopher F. Novak. Discontinuity-growth of interval-exchange maps. Journal of Modern Dynamics, 2009, 3 (3) : 379-405. doi: 10.3934/jmd.2009.3.379 |
[7] |
Woochul Jung, Ngocthach Nguyen, Yinong Yang. Spectral decomposition for rescaling expansive flows with rescaled shadowing. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2267-2283. doi: 10.3934/dcds.2020113 |
[8] |
Tatsuya Arai. The structure of dendrites constructed by pointwise P-expansive maps on the unit interval. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 43-61. doi: 10.3934/dcds.2016.36.43 |
[9] |
José Ginés Espín Buendía, Daniel Peralta-salas, Gabriel Soler López. Existence of minimal flows on nonorientable surfaces. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4191-4211. doi: 10.3934/dcds.2017178 |
[10] |
Davit Karagulyan. Hausdorff dimension of a class of three-interval exchange maps. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1257-1281. doi: 10.3934/dcds.2020077 |
[11] |
Alfonso Artigue. Discrete and continuous topological dynamics: Fields of cross sections and expansive flows. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 5911-5927. doi: 10.3934/dcds.2016059 |
[12] |
Artur O. Lopes, Vladimir A. Rosas, Rafael O. Ruggiero. Cohomology and subcohomology problems for expansive, non Anosov geodesic flows. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 403-422. doi: 10.3934/dcds.2007.17.403 |
[13] |
Jan Philipp Schröder. Ergodicity and topological entropy of geodesic flows on surfaces. Journal of Modern Dynamics, 2015, 9: 147-167. doi: 10.3934/jmd.2015.9.147 |
[14] |
Dmitri Scheglov. Absence of mixing for smooth flows on genus two surfaces. Journal of Modern Dynamics, 2009, 3 (1) : 13-34. doi: 10.3934/jmd.2009.3.13 |
[15] |
Keith Burns, Katrin Gelfert. Lyapunov spectrum for geodesic flows of rank 1 surfaces. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1841-1872. doi: 10.3934/dcds.2014.34.1841 |
[16] |
Dong Han Kim. The dynamical Borel-Cantelli lemma for interval maps. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 891-900. doi: 10.3934/dcds.2007.17.891 |
[17] |
Dong Han Kim, Luca Marchese, Stefano Marmi. Long hitting time for translation flows and L-shaped billiards. Journal of Modern Dynamics, 2019, 14: 291-353. doi: 10.3934/jmd.2019011 |
[18] |
Jacek Brzykcy, Krzysztof Frączek. Disjointness of interval exchange transformations from systems of probabilistic origin. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 53-73. doi: 10.3934/dcds.2010.27.53 |
[19] |
Lucia D. Simonelli. Absolutely continuous spectrum for parabolic flows/maps. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 263-292. doi: 10.3934/dcds.2018013 |
[20] |
David Ralston, Serge Troubetzkoy. Ergodic infinite group extensions of geodesic flows on translation surfaces. Journal of Modern Dynamics, 2012, 6 (4) : 477-497. doi: 10.3934/jmd.2012.6.477 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]