We construct symplectomorphisms in dimension d ≥ 4 having a semi-local robustly transitive partially hyperbolic set containing C2-robust homoclinic tangencies of any codimension $c$ with 0 < c ≤ d/2.
Citation: |
[1] |
E. Akin,
The General Topology of Dynamical Systems, vol. 1 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 1993.
![]() ![]() |
[2] |
A. Arbieto and C. Matheus, A pasting lemma and some applications for conservative systems, Ergodic Theory Dynam. Systems, 27 (2007), 1399-1417, With an appendix by David Diica and Yakov Simpson-Weller.
doi: 10.1017/S014338570700017X.![]() ![]() ![]() |
[3] |
V. I. Arnold, Instability of dynamical systems with many degrees of freedom, Dokl. Akad. Nauk SSSR, 156 (1964), 9-12.
![]() ![]() |
[4] |
A. Avila, J. Santamaria and M. Viana, Holonomy invariance: rough regularity and applications to lyapunov exponents, Astérisque, 358 (2013), 13-74.
![]() ![]() |
[5] |
A. Avila and M. Viana, Extremal Lyapunov exponents: An invariance principle and applications, Invent. Math., 181 (2010), 115-189.
doi: 10.1007/s00222-010-0243-1.![]() ![]() ![]() |
[6] |
P. G. Barrientos, Y. Ki and A. Raibekas, Symbolic blender-horseshoes and applications, Nonlinearity, 27 (2014), 2805-2839.
doi: 10.1088/0951-7715/27/12/2805.![]() ![]() ![]() |
[7] |
P. G. Barrientos and A. Raibekas, Robust tangencies of large codimension, Nonlinearity, 30 (2017), 4369-4409.
doi: 10.1088/1361-6544/aa8818.![]() ![]() ![]() |
[8] |
C. Bonatti and L. J. Díaz, Robust heterodimensional cycles and C1-generic dynamics, J. Inst. Math. Jussieu, 7 (2008), 469-525.
doi: 10.1017/S1474748008000030.![]() ![]() ![]() |
[9] |
C. Bonatti and L. J. Díaz, Abundance of C1-homoclinic tangencies, Trans. Amer. Math. Soc., 364 (2012), 5111-5148.
doi: 10.1090/S0002-9947-2012-05445-6.![]() ![]() ![]() |
[10] |
C. Bonatti and L. J. Díaz, Persistent nonhyperbolic transitive diffeomorphisms, Ann. of Math.(2), 143 (1996), 357-396.
doi: 10.2307/2118647.![]() ![]() ![]() |
[11] |
J. Buzzi, S. Crovisier and T. Fisher, Local perturbations of conservative C1 diffeomorphisms, Nonlinearity, 30 (2017), 3613-3636.
doi: 10.1088/1361-6544/aa803f.![]() ![]() ![]() |
[12] |
O. Castejón, M. Guardia and V. Kaloshin,
Random iteration of cylinder maps and diffusive behavior away from resonances,
arXiv: 1705.09571.
![]() |
[13] |
R. de la Llave, Orbits of unbounded energy in perturbations of geodesic flow by potentials. a simple construction, 2002, Preprint.
![]() |
[14] |
A. Delshams, R. de la Llave and T. M. Seara, A geometric mechanism for diffusion in
hamiltonian systems overcoming the large gap problem:
heuristics and rigorous verification on a model, Mem. Amer. Math. Soc., 179 (2006), 1-141.
doi: 10.1090/memo/0844.![]() ![]() ![]() |
[15] |
P. Duarte, Abundance of elliptic islands at conservative bifurcations, Dynamics and Stability of Systems, 14 (1999), 339-356.
doi: 10.1080/026811199281930.![]() ![]() ![]() |
[16] |
P. Duarte, Persistent homoclinic tangencies for conservative maps near the identity, Ergodic Theory Dynam. Systems, 20 (2000), 393-438.
doi: 10.1017/S0143385700000195.![]() ![]() ![]() |
[17] |
C.-W. Ho, On the periodic points of functions on a manifold, Proc. Amer. Math. Soc., 130 (2002), 2625-2630.
doi: 10.1090/S0002-9939-02-06361-X.![]() ![]() ![]() |
[18] |
A. J. Homburg and M. Nassiri, Robust minimality of iterated function systems with two generators, Ergodic Theory and Dynamical Systems, 34 (2014), 1914-1929.
doi: 10.1017/etds.2013.34.![]() ![]() ![]() |
[19] |
I. M. James, On category, in the sense of Lusternik-Schnirelmann, Topology, 17 (1978), 331-348.
doi: 10.1016/0040-9383(78)90002-2.![]() ![]() ![]() |
[20] |
J. M. Lee,
Introduction to Smooth Manifolds, vol. 218 of Graduate Texts in Mathematics, 2nd edition, Springer, New York, 2013.
![]() ![]() |
[21] |
J. Margalef-Roig and E. Dominguez,
Differential Topology, North-Holland Mathematics Studies, Elsevier Science, 1992, https://books.google.cl/books?id=gexAr04vRT4C.
![]() |
[22] |
D. G. Schaeffer and M. Golubitsky,
Singularities and Groups in Bifurcation Theory, Springer-Verlag, New York, 1985.
doi: 10.1007/978-1-4612-5034-0.![]() ![]() ![]() |
[23] |
L. Mora and N. Romero, Persistence of homoclinic tangencies for area-preserving maps, Annales de la Faculté des Sciences de Toulouse, 6 (1997), 711-725.
doi: 10.5802/afst.885.![]() ![]() ![]() |
[24] |
M. Nassiri and E. R. Pujals, Robust transitivity in hamiltonian dynamics, Ann. Sci. Éc. Norm. Supér., 45 (2012), 191-239.
doi: 10.24033/asens.2164.![]() ![]() ![]() |
[25] |
S. E. Newhouse, Nondensity of axiom A(a) on S2, in Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970,191-202.
doi: 10.1007/978-3-642-16830-7.![]() ![]() ![]() |
[26] |
J. Ombach, Shadowing, expansiveness and hyperbolic homeomorphisms, J. Austral. Math. Soc. Ser. A, 61 (1996), 57-72.
doi: 10.1017/S1446788700000070.![]() ![]() ![]() |