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On the set of periods of sigma maps of degree 1
Topological properties of sectional-Anosov flows
1. | Departamento de Matemática, Universidade Federal de Viçosa, Viçosa-MG, Brazil, Brazil |
2. | Departamento de Matemática, Universidade Federal do Rio de Janeiro, RJ, Brazil |
References:
[1] |
S. Bautista and C. A. Morales, Existence of periodic orbits for singular-hyperbolic sets, Mosc. Math. J., 6 (2006), 265-297, 406. |
[2] |
J. S. Birman and R. F. Williams, Knotted periodic orbits in dynamical system. II. Knot holders for fibered knots, in Low-Dimensional Topology (San Francisco, Calif., 1981), Contemp. Math., 20, Amer. Math. Soc., Providence, RI, 1983, 1-60.
doi: 10.1090/conm/020/718132. |
[3] |
C. Bonatti, A. Pumariño and M. Viana, Lorenz attractors with arbitrary expanding dimension, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 883-888.
doi: 10.1016/S0764-4442(97)80131-0. |
[4] |
H. G. Bothe, How hyperbolic attractors determine their basins, Nonlinearity, 9 (1996), 1173-1190.
doi: 10.1088/0951-7715/9/5/006. |
[5] |
H. G. Bothe, Strange attractors with topologically simple basins, Topology Appl., 114 (2001), 1-25.
doi: 10.1016/S0166-8641(00)00034-1. |
[6] |
C. Camacho and A. Lins Neto, Geometric Theory of Foliations, Birkhäuser Boston, Inc., Boston, MA, 1985.
doi: 10.1007/978-1-4612-5292-4. |
[7] |
J. Franks and B. Williams, Anomalous Anosov flows, in Global Theory of Dynamical Systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979), Lecture Notes in Math., 819, Springer, Berlin, 1980, 158-174. |
[8] |
J. Guckenheimer and R. F. Williams, Structural stability of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 59-72. |
[9] |
G. Hector and U. Hirsch, Introduction to the Geometry of Foliations, Parts A and B, Vieweg, Braunschweig, 1986.
doi: 10.1007/978-3-322-90115-6. |
[10] |
J. Hempel, 3-Manifolds, Ann. of Math. Studies, No. 86, Princeton University Press, Princeton, N.J., University of Tokyo Press, Tokyo, 1976. |
[11] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, Berlin-New York, 1977. |
[12] |
R. Metzger and C. A. Morales, Sectional-hyperbolic system, Ergod. Th. Dynam. Sys., 28 (2008), 1587-1597.
doi: 10.1017/S0143385707000995. |
[13] |
J. Milnor, Topology from the Differentiable Viewpoint, Based on notes by David W. Weaver The University Press of Virginia, Charlottesville, Va., 1965. |
[14] |
C. A. Morales, Sectional-Anosov flows, Monatsh. Math., 159 (2010), 253-260.
doi: 10.1007/s00605-008-0078-7. |
[15] |
C. A. Morales, Incompressibility of tori transverse to Axiom A flows, Proc. Amer. Math. Soc., 136 (2008), 4349-4354.
doi: 10.1090/S0002-9939-08-09409-4. |
[16] |
C. A. Morales, Singular-hyperbolic attractors with handlebody basins, J. Dyn. Control Syst., 13 (2007), 15-24.
doi: 10.1007/s10883-006-9000-6. |
[17] |
C. A. Morales, M. J. Pacifico and E. R. Pujals, Singular hyperbolic systems, Proc. Amer. Math. Soc., 127 (1999), 3393-3401.
doi: 10.1090/S0002-9939-99-04936-9. |
[18] |
S. Novikov, Topology of Foliations, Trudy Mosk. Mat. Obbsh., 14 (1965), 248-278 (AMS, translation 1967). |
[19] |
J. F. Plante and W. P. Thurston, Anosov flows and the fundamental group, Topology, 11 (1972), 147-150.
doi: 10.1016/0040-9383(72)90002-X. |
[20] |
J. E. Reis, Infinidade de órbitas periódicas para fluxos seccional-Anosov, Tese (doutorado) - UFRJ/ IM/ Programa de Pós- Graduação em Matemática, 2011. |
[21] |
B. Scárdua and J. Seade, Codimension one foliations with Bott-Morse singularities. I, J. Differential Geom., 83 (2009), 189-212. |
[22] |
T. Sodero, Sectional-Anosov flows on certain compact 3-manifolds, Bull. Braz. Math. Soc. (N.S.), 42 (2011), 439-454.
doi: 10.1007/s00574-011-0024-5. |
[23] |
T. Vivier, Projective hyperbolicity and fixed points, Ergodic Theory Dynam. Systems, 26 (2006), 923-936.
doi: 10.1017/S0143385705000581. |
show all references
References:
[1] |
S. Bautista and C. A. Morales, Existence of periodic orbits for singular-hyperbolic sets, Mosc. Math. J., 6 (2006), 265-297, 406. |
[2] |
J. S. Birman and R. F. Williams, Knotted periodic orbits in dynamical system. II. Knot holders for fibered knots, in Low-Dimensional Topology (San Francisco, Calif., 1981), Contemp. Math., 20, Amer. Math. Soc., Providence, RI, 1983, 1-60.
doi: 10.1090/conm/020/718132. |
[3] |
C. Bonatti, A. Pumariño and M. Viana, Lorenz attractors with arbitrary expanding dimension, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 883-888.
doi: 10.1016/S0764-4442(97)80131-0. |
[4] |
H. G. Bothe, How hyperbolic attractors determine their basins, Nonlinearity, 9 (1996), 1173-1190.
doi: 10.1088/0951-7715/9/5/006. |
[5] |
H. G. Bothe, Strange attractors with topologically simple basins, Topology Appl., 114 (2001), 1-25.
doi: 10.1016/S0166-8641(00)00034-1. |
[6] |
C. Camacho and A. Lins Neto, Geometric Theory of Foliations, Birkhäuser Boston, Inc., Boston, MA, 1985.
doi: 10.1007/978-1-4612-5292-4. |
[7] |
J. Franks and B. Williams, Anomalous Anosov flows, in Global Theory of Dynamical Systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979), Lecture Notes in Math., 819, Springer, Berlin, 1980, 158-174. |
[8] |
J. Guckenheimer and R. F. Williams, Structural stability of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 59-72. |
[9] |
G. Hector and U. Hirsch, Introduction to the Geometry of Foliations, Parts A and B, Vieweg, Braunschweig, 1986.
doi: 10.1007/978-3-322-90115-6. |
[10] |
J. Hempel, 3-Manifolds, Ann. of Math. Studies, No. 86, Princeton University Press, Princeton, N.J., University of Tokyo Press, Tokyo, 1976. |
[11] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, Berlin-New York, 1977. |
[12] |
R. Metzger and C. A. Morales, Sectional-hyperbolic system, Ergod. Th. Dynam. Sys., 28 (2008), 1587-1597.
doi: 10.1017/S0143385707000995. |
[13] |
J. Milnor, Topology from the Differentiable Viewpoint, Based on notes by David W. Weaver The University Press of Virginia, Charlottesville, Va., 1965. |
[14] |
C. A. Morales, Sectional-Anosov flows, Monatsh. Math., 159 (2010), 253-260.
doi: 10.1007/s00605-008-0078-7. |
[15] |
C. A. Morales, Incompressibility of tori transverse to Axiom A flows, Proc. Amer. Math. Soc., 136 (2008), 4349-4354.
doi: 10.1090/S0002-9939-08-09409-4. |
[16] |
C. A. Morales, Singular-hyperbolic attractors with handlebody basins, J. Dyn. Control Syst., 13 (2007), 15-24.
doi: 10.1007/s10883-006-9000-6. |
[17] |
C. A. Morales, M. J. Pacifico and E. R. Pujals, Singular hyperbolic systems, Proc. Amer. Math. Soc., 127 (1999), 3393-3401.
doi: 10.1090/S0002-9939-99-04936-9. |
[18] |
S. Novikov, Topology of Foliations, Trudy Mosk. Mat. Obbsh., 14 (1965), 248-278 (AMS, translation 1967). |
[19] |
J. F. Plante and W. P. Thurston, Anosov flows and the fundamental group, Topology, 11 (1972), 147-150.
doi: 10.1016/0040-9383(72)90002-X. |
[20] |
J. E. Reis, Infinidade de órbitas periódicas para fluxos seccional-Anosov, Tese (doutorado) - UFRJ/ IM/ Programa de Pós- Graduação em Matemática, 2011. |
[21] |
B. Scárdua and J. Seade, Codimension one foliations with Bott-Morse singularities. I, J. Differential Geom., 83 (2009), 189-212. |
[22] |
T. Sodero, Sectional-Anosov flows on certain compact 3-manifolds, Bull. Braz. Math. Soc. (N.S.), 42 (2011), 439-454.
doi: 10.1007/s00574-011-0024-5. |
[23] |
T. Vivier, Projective hyperbolicity and fixed points, Ergodic Theory Dynam. Systems, 26 (2006), 923-936.
doi: 10.1017/S0143385705000581. |
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