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2017, 24: 1-9.
doi: 10.3934/era.2017.24.001
Desingularization of surface maps
| 1. | Department of Mathematics, Tufts University, Medford, MA 02155, USA |
| 2. | IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brasil 22460-320 |
We prove a result for maps of surfaces that illustrates how singularhyperbolic flows can be desingularized if a global section can be collapsed to a surface along stable leaves.
Keywords:
Singularization,
hyperbolicity.
Mathematics Subject Classification:
Primary: 37D20; Secondary: 57N10.
Citation:
Erica Clay, Boris Hasselblatt, Enrique Pujals. Desingularization of surface maps. Electronic Research Announcements,
2017, 24: 1-9.
doi: 10.3934/era.2017.24.001
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References:
| [1] |
C. Bonatti, L. J. Díaz and M. Viana, Dynamics Beyond Uniform Hyperbolicity. A Global Geometric and Probabilistic Perspective, Encyclopaedia of Mathematical Sciences, 102, Mathematical Physics, Ⅲ, Springer-Verlag, Berlin, 2005. |
| [2] |
C. Bonatti, A. Pumariño and M. Viana,
Lorenz attractors with arbitrary expanding dimension, C. R. Acad. Paris Sér. I Math., 325 (1997), 883-888.
doi: 10.1016/S0764-4442(97)80131-0. |
| [3] |
R. J. Daverman and G. A. Venema, Embeddings in Manifolds, Graduate Studies in Mathematics, 106, American Mathematical Society, Providence, RI, 2009.
doi: 10.1090/gsm/106. |
| [4] |
B. Hasselblatt and A. Katok, A First Course in Dynamics. With a Panorama of Recent Developments, Cambridge University Press, New York, 2003. |
| [5] |
C. A. Morales and M. J. Pacifico, Strange attractors arising from hyperbolic flows, preprint. |
| [6] |
C. A. Morales, M. J. Pacifico and E. R. Pujals,
Global attractors from the explosion of singular cycles, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 1317-1322.
doi: 10.1016/S0764-4442(97)82362-2. |
| [7] |
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. |
| [8] |
R. Metzger and C. Morales,
Sectional-Hyperbolic Systems, Ergodic Theory Dynam. Systems, 28 (2008), 1587-1597.
doi: 10.1017/S0143385707000995. |
| [9] |
S. Newhouse, On simple arcs between structurally stable flows, in Dynamical SystemsWarwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E. C. Zeeman on his fiftieth birthday), Lecture Notes in Math., Vol. 468, Springer, Berlin, 1975,209-233. |
| [10] |
S. Smale,
Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
doi: 10.1090/S0002-9904-1967-11798-1. |
show all references
References:
| [1] |
C. Bonatti, L. J. Díaz and M. Viana, Dynamics Beyond Uniform Hyperbolicity. A Global Geometric and Probabilistic Perspective, Encyclopaedia of Mathematical Sciences, 102, Mathematical Physics, Ⅲ, Springer-Verlag, Berlin, 2005. |
| [2] |
C. Bonatti, A. Pumariño and M. Viana,
Lorenz attractors with arbitrary expanding dimension, C. R. Acad. Paris Sér. I Math., 325 (1997), 883-888.
doi: 10.1016/S0764-4442(97)80131-0. |
| [3] |
R. J. Daverman and G. A. Venema, Embeddings in Manifolds, Graduate Studies in Mathematics, 106, American Mathematical Society, Providence, RI, 2009.
doi: 10.1090/gsm/106. |
| [4] |
B. Hasselblatt and A. Katok, A First Course in Dynamics. With a Panorama of Recent Developments, Cambridge University Press, New York, 2003. |
| [5] |
C. A. Morales and M. J. Pacifico, Strange attractors arising from hyperbolic flows, preprint. |
| [6] |
C. A. Morales, M. J. Pacifico and E. R. Pujals,
Global attractors from the explosion of singular cycles, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 1317-1322.
doi: 10.1016/S0764-4442(97)82362-2. |
| [7] |
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. |
| [8] |
R. Metzger and C. Morales,
Sectional-Hyperbolic Systems, Ergodic Theory Dynam. Systems, 28 (2008), 1587-1597.
doi: 10.1017/S0143385707000995. |
| [9] |
S. Newhouse, On simple arcs between structurally stable flows, in Dynamical SystemsWarwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E. C. Zeeman on his fiftieth birthday), Lecture Notes in Math., Vol. 468, Springer, Berlin, 1975,209-233. |
| [10] |
S. Smale,
Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
doi: 10.1090/S0002-9904-1967-11798-1. |
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