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Smooth deformations of piecewise expanding unimodal maps
Covering relations and the existence of topologically normally hyperbolic invariant sets
1. | AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland |
[1] |
Maciej J. Capiński, Piotr Zgliczyński. Cone conditions and covering relations for topologically normally hyperbolic invariant manifolds. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 641-670. doi: 10.3934/dcds.2011.30.641 |
[2] |
Evelyn Sander. Hyperbolic sets for noninvertible maps and relations. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 339-357. doi: 10.3934/dcds.1999.5.339 |
[3] |
Maciej J. Capiński, Piotr Zgliczyński. Covering relations and non-autonomous perturbations of ODEs. Discrete and Continuous Dynamical Systems, 2006, 14 (2) : 281-293. doi: 10.3934/dcds.2006.14.281 |
[4] |
Henk Broer, Aaron Hagen, Gert Vegter. Numerical approximation of normally hyperbolic invariant manifolds. Conference Publications, 2003, 2003 (Special) : 133-140. doi: 10.3934/proc.2003.2003.133 |
[5] |
Amadeu Delshams, Marian Gidea, Pablo Roldán. Transition map and shadowing lemma for normally hyperbolic invariant manifolds. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1089-1112. doi: 10.3934/dcds.2013.33.1089 |
[6] |
Jean-François Biasse. Subexponential time relations in the class group of large degree number fields. Advances in Mathematics of Communications, 2014, 8 (4) : 407-425. doi: 10.3934/amc.2014.8.407 |
[7] |
Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco. Linear nonbinary covering codes and saturating sets in projective spaces. Advances in Mathematics of Communications, 2011, 5 (1) : 119-147. doi: 10.3934/amc.2011.5.119 |
[8] |
Todd Fisher. Hyperbolic sets with nonempty interior. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 433-446. doi: 10.3934/dcds.2006.15.433 |
[9] |
Marian Gidea, Rafael de la Llave, Tere M. Seara. A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6795-6813. doi: 10.3934/dcds.2020166 |
[10] |
Adriano Da Silva, Christoph Kawan. Invariance entropy of hyperbolic control sets. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 97-136. doi: 10.3934/dcds.2016.36.97 |
[11] |
Mario Roldan. Hyperbolic sets and entropy at the homological level. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3417-3433. doi: 10.3934/dcds.2016.36.3417 |
[12] |
Zhihong Xia. Hyperbolic invariant sets with positive measures. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 811-818. doi: 10.3934/dcds.2006.15.811 |
[13] |
Serafin Bautista, Carlos A. Morales. On the intersection of sectional-hyperbolic sets. Journal of Modern Dynamics, 2015, 9: 203-218. doi: 10.3934/jmd.2015.9.203 |
[14] |
Boris Hasselblatt and Jorg Schmeling. Dimension product structure of hyperbolic sets. Electronic Research Announcements, 2004, 10: 88-96. |
[15] |
Lorenzo Arona, Josep J. Masdemont. Computation of heteroclinic orbits between normally hyperbolic invariant 3-spheres foliated by 2-dimensional invariant Tori in Hill's problem. Conference Publications, 2007, 2007 (Special) : 64-74. doi: 10.3934/proc.2007.2007.64 |
[16] |
Adriana da Luz. Hyperbolic sets that are not contained in a locally maximal one. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 4923-4941. doi: 10.3934/dcds.2017166 |
[17] |
Carlos Arnoldo Morales. Strong stable manifolds for sectional-hyperbolic sets. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 553-560. doi: 10.3934/dcds.2007.17.553 |
[18] |
Luiz Felipe Nobili França. Partially hyperbolic sets with a dynamically minimal lamination. Discrete and Continuous Dynamical Systems, 2018, 38 (6) : 2717-2729. doi: 10.3934/dcds.2018114 |
[19] |
A. M. López. Finiteness and existence of attractors and repellers on sectional hyperbolic sets. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 337-354. doi: 10.3934/dcds.2017014 |
[20] |
Xiao Wen, Lan Wen. No-shadowing for singular hyperbolic sets with a singularity. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 6043-6059. doi: 10.3934/dcds.2020258 |
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