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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.
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.
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.
doi: 10.1007/BF02099308. |
[4] |
C. Gutiérrez, Smoothability of Cherry flows on two-manifolds,, In Lecture Notes in Math, 1007 (1983), 308.
doi: 10.1007/BFb0061422. |
[5] |
C. Gutiérrez, Smoothing continuous flows on two-manifolds and recurrences,, Ergodic Theory Dynam. Systems, 6 (1986), 17.
|
[6] |
P. Hartman, "Ordinary Differential Equations,'', John Wiley & Sons Inc., (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.
|
[8] |
K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov,, Osaka J. Math, 27 (1990), 117.
|
[9] |
M. W. Hirsch, "Differential Topology,'', Graduate Texts in Mathematics, (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.
|
[11] |
M. Keane, Interval exchange transformations,, Math. Z., 141 (1975), 25.
doi: 10.1007/BF01236981. |
[12] |
M. Komuro, Expansive properties of Lorenz attractors,, The theory of dynamical systems and its applications to nonlinear problems, (1984), 4.
|
[13] |
J. Lewowicz, Expansive homeomorphisms of surfaces,, Bol. Soc. Brasil. Mat. (N.S.), 20 (1989), 113.
doi: 10.1007/BF02585472. |
[14] |
N. G. Markley, On the number of recurrent orbit closures,, Proc. Amer. Math. Soc., 25 (1970), 413.
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.
|
[16] |
M. Oka, Expansiveness of real flows,, Tsukuba J. Math, 14 (1990), 1.
|
[17] |
H. Whitney, Regular families of curves,, Ann. of Math, 34 (1933), 244.
doi: 10.2307/1968202. |
[18] |
A. N. Zemljakov and A. B. Katok, Topological transitivity of billiards in polygons,, Mat. Zametki, 18 (1975), 291.
|
show all references
References:
[1] |
R. Bowen and P. Walters, Expansive one-parameter flows,, J. Differential Equations, 12 (1972), 180.
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.
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.
doi: 10.1007/BF02099308. |
[4] |
C. Gutiérrez, Smoothability of Cherry flows on two-manifolds,, In Lecture Notes in Math, 1007 (1983), 308.
doi: 10.1007/BFb0061422. |
[5] |
C. Gutiérrez, Smoothing continuous flows on two-manifolds and recurrences,, Ergodic Theory Dynam. Systems, 6 (1986), 17.
|
[6] |
P. Hartman, "Ordinary Differential Equations,'', John Wiley & Sons Inc., (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.
|
[8] |
K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov,, Osaka J. Math, 27 (1990), 117.
|
[9] |
M. W. Hirsch, "Differential Topology,'', Graduate Texts in Mathematics, (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.
|
[11] |
M. Keane, Interval exchange transformations,, Math. Z., 141 (1975), 25.
doi: 10.1007/BF01236981. |
[12] |
M. Komuro, Expansive properties of Lorenz attractors,, The theory of dynamical systems and its applications to nonlinear problems, (1984), 4.
|
[13] |
J. Lewowicz, Expansive homeomorphisms of surfaces,, Bol. Soc. Brasil. Mat. (N.S.), 20 (1989), 113.
doi: 10.1007/BF02585472. |
[14] |
N. G. Markley, On the number of recurrent orbit closures,, Proc. Amer. Math. Soc., 25 (1970), 413.
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.
|
[16] |
M. Oka, Expansiveness of real flows,, Tsukuba J. Math, 14 (1990), 1.
|
[17] |
H. Whitney, Regular families of curves,, Ann. of Math, 34 (1933), 244.
doi: 10.2307/1968202. |
[18] |
A. N. Zemljakov and A. B. Katok, Topological transitivity of billiards in polygons,, Mat. Zametki, 18 (1975), 291.
|
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