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On the Hausdorff dimension of the Sierpiński Julia sets
Density of the set of endomorphisms with a maximizing measure supported on a periodic orbit
1. | Universidade Tecnológica Federal do Paraná - UTFPR, Av. Professora Laura Pacheco Bastos, 800 - Bairro Industrial, 85053-525, Guarapuava-PR, Brazil, Brazil |
2. | Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo, SP, Brazil |
References:
[1] |
S. Addas-Zanata and F. A. Tal, Support of maximizing measures for typical $\mathcalC^0$ dynamics on compact manifolds, Discrete Contin. Dyn. Syst., 26 (2010), 795-804.
doi: 10.3934/dcds.2010.26.795. |
[2] |
S. Addas-Zanata and F. A. Tal, Maximizing measures for endomorphisms of the circle, Nonlinearity, 21 (2008), 2347-2359.
doi: 10.1088/0951-7715/21/10/008. |
[3] |
S. Addas-Zanata and F. A. Tal, On maximizing measures of homeomorphisms on compact manifolds, Fund. Math., 200 (2008), 145-159.
doi: 10.4064/fm200-2-3. |
[4] |
G. Atkinson, Recurrence of cocycles and random walks, J. London Math. Soc., 13 (1976), 486-488. |
[5] |
T. Bousch, La condition de Walters, Ann. Sci. École Norm. Sup. (4), 34 (2001), 287-311.
doi: 10.1016/S0012-9593(00)01062-4. |
[6] |
G. Contreras, A. O. Lopes and P. Thieullen, Lyapunov minimizing measures for expanding maps of the circle, Ergodic Theory Dynam. Systems, 21 (2001), 1379-1409.
doi: 10.1017/S0143385701001663. |
[7] |
G. Contreras, J. Delgado and R. Iturriaga, Lagrangian flows: The dynamics of globally minimizing orbits. II, Bol. Soc. Brasil. Mat. (N.S.), 28 (1997), 155-196.
doi: 10.1007/BF01233390. |
[8] |
J. P. Conze and Y. Guivarch, Croissance des sommes ergodiques et principe variationnel, 1993, Manuscript. |
[9] |
E. Garibaldi and P. Thieullen, Minimizing orbits in the discrete Aubry-Mather model, Nonlinearity, 24 (2011), 563-611.
doi: 10.1088/0951-7715/24/2/008. |
[10] |
O. Jenkinson, Ergodic optimization, Discrete Contin. Dyn. Syst., 15 (2006), 197-224.
doi: 10.3934/dcds.2006.15.197. |
[11] |
O. Jenkinson and I. D. Morris, Lyapunov optimizing measures for $C^1$ expanding maps of the circle, Ergodic Theory Dynam. Systems, 28 (2008), 1849-1860.
doi: 10.1017/S0143385708000333. |
[12] |
A. O. Lopes and P. Thieullen, Sub-actions for Anosov diffeomorphisms, Astérisque, xix, Geometric methods in dynamics. II (2003), 135-146. |
[13] |
I. D. Morris, Ergodic optimization for generic continuous functions, Discrete Contin. Dyn. Syst., 27 (2010), 383-388.
doi: 10.3934/dcds.2010.27.383. |
show all references
References:
[1] |
S. Addas-Zanata and F. A. Tal, Support of maximizing measures for typical $\mathcalC^0$ dynamics on compact manifolds, Discrete Contin. Dyn. Syst., 26 (2010), 795-804.
doi: 10.3934/dcds.2010.26.795. |
[2] |
S. Addas-Zanata and F. A. Tal, Maximizing measures for endomorphisms of the circle, Nonlinearity, 21 (2008), 2347-2359.
doi: 10.1088/0951-7715/21/10/008. |
[3] |
S. Addas-Zanata and F. A. Tal, On maximizing measures of homeomorphisms on compact manifolds, Fund. Math., 200 (2008), 145-159.
doi: 10.4064/fm200-2-3. |
[4] |
G. Atkinson, Recurrence of cocycles and random walks, J. London Math. Soc., 13 (1976), 486-488. |
[5] |
T. Bousch, La condition de Walters, Ann. Sci. École Norm. Sup. (4), 34 (2001), 287-311.
doi: 10.1016/S0012-9593(00)01062-4. |
[6] |
G. Contreras, A. O. Lopes and P. Thieullen, Lyapunov minimizing measures for expanding maps of the circle, Ergodic Theory Dynam. Systems, 21 (2001), 1379-1409.
doi: 10.1017/S0143385701001663. |
[7] |
G. Contreras, J. Delgado and R. Iturriaga, Lagrangian flows: The dynamics of globally minimizing orbits. II, Bol. Soc. Brasil. Mat. (N.S.), 28 (1997), 155-196.
doi: 10.1007/BF01233390. |
[8] |
J. P. Conze and Y. Guivarch, Croissance des sommes ergodiques et principe variationnel, 1993, Manuscript. |
[9] |
E. Garibaldi and P. Thieullen, Minimizing orbits in the discrete Aubry-Mather model, Nonlinearity, 24 (2011), 563-611.
doi: 10.1088/0951-7715/24/2/008. |
[10] |
O. Jenkinson, Ergodic optimization, Discrete Contin. Dyn. Syst., 15 (2006), 197-224.
doi: 10.3934/dcds.2006.15.197. |
[11] |
O. Jenkinson and I. D. Morris, Lyapunov optimizing measures for $C^1$ expanding maps of the circle, Ergodic Theory Dynam. Systems, 28 (2008), 1849-1860.
doi: 10.1017/S0143385708000333. |
[12] |
A. O. Lopes and P. Thieullen, Sub-actions for Anosov diffeomorphisms, Astérisque, xix, Geometric methods in dynamics. II (2003), 135-146. |
[13] |
I. D. Morris, Ergodic optimization for generic continuous functions, Discrete Contin. Dyn. Syst., 27 (2010), 383-388.
doi: 10.3934/dcds.2010.27.383. |
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