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On the stability of some properly--degenerate Hamiltonian systems with two degrees of freedom
Pointwise dimensions for Poincaré recurrences associated with maps and special flows
1. | IICO-UASLP, A. Obregón 64, 78000 San Luis Postosí, SLP, Mexico |
2. | Centre de Physique Théorique, CNRS-Ecole polytechnique, UMR 7644, F-91128 Palaiseau Cedex, France |
3. | CNRS-LAMFA, Université de Picardie Jules Verne, 80039 Amiens, France |
[1] |
V. Afraimovich, J. Schmeling, Edgardo Ugalde, Jesús Urías. Spectra of dimensions for Poincaré recurrences. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 901-914. doi: 10.3934/dcds.2000.6.901 |
[2] |
B. Fernandez, E. Ugalde, J. Urías. Spectrum of dimensions for Poincaré recurrences of Markov maps. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 835-849. doi: 10.3934/dcds.2002.8.835 |
[3] |
Valentin Afraimovich, Jean-Rene Chazottes and Benoit Saussol. Local dimensions for Poincare recurrences. Electronic Research Announcements, 2000, 6: 64-74. |
[4] |
João Lopes Dias. Brjuno condition and renormalization for Poincaré flows. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 641-656. doi: 10.3934/dcds.2006.15.641 |
[5] |
Aleksander Ćwiszewski, Wojciech Kryszewski. On a generalized Poincaré-Hopf formula in infinite dimensions. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 953-978. doi: 10.3934/dcds.2011.29.953 |
[6] |
Oliver Butterley, Carlangelo Liverani. Smooth Anosov flows: Correlation spectra and stability. Journal of Modern Dynamics, 2007, 1 (2) : 301-322. doi: 10.3934/jmd.2007.1.301 |
[7] |
Yongqin Liu, Weike Wang. The pointwise estimates of solutions for dissipative wave equation in multi-dimensions. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1013-1028. doi: 10.3934/dcds.2008.20.1013 |
[8] |
Eugen Mihailescu. Equilibrium measures, prehistories distributions and fractal dimensions for endomorphisms. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 2485-2502. doi: 10.3934/dcds.2012.32.2485 |
[9] |
Luis Barreira, Yakov Pesin and Jorg Schmeling. On the pointwise dimension of hyperbolic measures: a proof of the Eckmann-Ruelle conjecture. Electronic Research Announcements, 1996, 2: 69-72. |
[10] |
Przemysław Berk, Krzysztof Frączek. On special flows over IETs that are not isomorphic to their inverses. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 829-855. doi: 10.3934/dcds.2015.35.829 |
[11] |
Boris Khesin, Fedor Soloviev. The pentagram map in higher dimensions and KdV flows. Electronic Research Announcements, 2012, 19: 86-96. doi: 10.3934/era.2012.19.86 |
[12] |
Wenyu Pan. Joining measures for horocycle flows on abelian covers. Journal of Modern Dynamics, 2018, 12: 17-54. doi: 10.3934/jmd.2018003 |
[13] |
Radu Saghin. On the number of ergodic minimizing measures for Lagrangian flows. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 501-507. doi: 10.3934/dcds.2007.17.501 |
[14] |
Hiroki Sumi, Mariusz Urbański. Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 313-363. doi: 10.3934/dcds.2011.30.313 |
[15] |
Moisey Guysinsky, Serge Yaskolko. Coincidence of various dimensions associated with metrics and measures on metric spaces. Discrete and Continuous Dynamical Systems, 1997, 3 (4) : 591-603. doi: 10.3934/dcds.1997.3.591 |
[16] |
Fawwaz Batayneh, Cecilia González-Tokman. On the number of invariant measures for random expanding maps in higher dimensions. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 5887-5914. doi: 10.3934/dcds.2021100 |
[17] |
Niklas Behringer. Improved error estimates for optimal control of the Stokes problem with pointwise tracking in three dimensions. Mathematical Control and Related Fields, 2021, 11 (2) : 313-328. doi: 10.3934/mcrf.2020038 |
[18] |
Zhigang Wu, Weike Wang. Pointwise estimates of solutions for the Euler-Poisson equations with damping in multi-dimensions. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 1101-1117. doi: 10.3934/dcds.2010.26.1101 |
[19] |
Bassam Fayad, A. Windsor. A dichotomy between discrete and continuous spectrum for a class of special flows over rotations. Journal of Modern Dynamics, 2007, 1 (1) : 107-122. doi: 10.3934/jmd.2007.1.107 |
[20] |
Krzysztof Frączek, M. Lemańczyk, E. Lesigne. Mild mixing property for special flows under piecewise constant functions. Discrete and Continuous Dynamical Systems, 2007, 19 (4) : 691-710. doi: 10.3934/dcds.2007.19.691 |
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