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Stochastic adding machine and $2$-dimensional Julia sets
1. | UNESP - Departamento de Matemática do, Instituto de Biociências, Letras e Ciências, Exatas de São José do Rio Preto, Brazil |
2. | Université de Picardie Jules Verne, Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS - UMR 7352, France |
References:
[1] |
E. H. El Abdalaoui and A. Messaoudi, On the spectrum of stochastic perturbations of the shift map and Julia sets, Fundamenta Mathematicae, 218 (2012), 47-68.
doi: 10.4064/fm218-1-3. |
[2] |
El Abdalaoui, S. Bonnot, A. Messaoudi and O. Sester, On the Fibonacci Complex Dynamical Systems, arXiv:1304.4864, 26p, 2013. |
[3] |
E. Bedford and J. Smillie, John Polynomial diffeomorphisms of $\mathbbC^2$ VI. Connectivity of J, Ann. of Math. (2), 148 (1998), 695-735.
doi: 10.2307/121006. |
[4] |
R. L. Devaney, An Introduction to Chaothic Dynamical Systems, ABP, 2003. |
[5] |
S. Eilenberg, Automata, Languages, and Machines, Volume 1, Academic Press, New York and London, 1974. |
[6] |
J. E. Fornaess and N. Sibony, Fatou and Julia sets for entire mappings in $\mathbbC^k$, Math. Ann., 311 (1998), 27-40.
doi: 10.1007/s002080050174. |
[7] |
A. S. Fraenkel, Systems of numeration, Amer. Math. Monthly, 92 (1985), 105-114.
doi: 10.2307/2322638. |
[8] |
C. Frougny, Representation of numbers and finite automata, Math. Systems Theory, 25 (1992), 37-60.
doi: 10.1007/BF01368783. |
[9] |
P. R. Killeen and T. J. Taylor, A stochastic adding machine and complex dynamics, Nonlinearity, 13 (2000), 1889-1903.
doi: 10.1088/0951-7715/13/6/302. |
[10] |
S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge University Press, 2000. |
[11] |
J. Milnor, Dynamics in One Complex Variable, Princeton University Press, 2006. |
[12] |
A. Messaoudi and D. Smania, Eigenvalues of Fibonacci stochastic adding machine, Stoch. Dyn., 10 (2010), 291-313.
doi: 10.1142/S0219493710002966. |
[13] |
A. Messaoudi, O. Sester and G. Valle, Spectrum of stochastic adding machine and fibred Julia sets, Stochastic and Dynamics, 13 (2013), 1250021, 26pp.
doi: 10.1142/S0219493712500219. |
[14] |
R. A. Uceda, Máquina de Somar, Conjuntos de Julia e Fractais de Rauzy, PhD Thesis, 2011. |
[15] |
show all references
References:
[1] |
E. H. El Abdalaoui and A. Messaoudi, On the spectrum of stochastic perturbations of the shift map and Julia sets, Fundamenta Mathematicae, 218 (2012), 47-68.
doi: 10.4064/fm218-1-3. |
[2] |
El Abdalaoui, S. Bonnot, A. Messaoudi and O. Sester, On the Fibonacci Complex Dynamical Systems, arXiv:1304.4864, 26p, 2013. |
[3] |
E. Bedford and J. Smillie, John Polynomial diffeomorphisms of $\mathbbC^2$ VI. Connectivity of J, Ann. of Math. (2), 148 (1998), 695-735.
doi: 10.2307/121006. |
[4] |
R. L. Devaney, An Introduction to Chaothic Dynamical Systems, ABP, 2003. |
[5] |
S. Eilenberg, Automata, Languages, and Machines, Volume 1, Academic Press, New York and London, 1974. |
[6] |
J. E. Fornaess and N. Sibony, Fatou and Julia sets for entire mappings in $\mathbbC^k$, Math. Ann., 311 (1998), 27-40.
doi: 10.1007/s002080050174. |
[7] |
A. S. Fraenkel, Systems of numeration, Amer. Math. Monthly, 92 (1985), 105-114.
doi: 10.2307/2322638. |
[8] |
C. Frougny, Representation of numbers and finite automata, Math. Systems Theory, 25 (1992), 37-60.
doi: 10.1007/BF01368783. |
[9] |
P. R. Killeen and T. J. Taylor, A stochastic adding machine and complex dynamics, Nonlinearity, 13 (2000), 1889-1903.
doi: 10.1088/0951-7715/13/6/302. |
[10] |
S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge University Press, 2000. |
[11] |
J. Milnor, Dynamics in One Complex Variable, Princeton University Press, 2006. |
[12] |
A. Messaoudi and D. Smania, Eigenvalues of Fibonacci stochastic adding machine, Stoch. Dyn., 10 (2010), 291-313.
doi: 10.1142/S0219493710002966. |
[13] |
A. Messaoudi, O. Sester and G. Valle, Spectrum of stochastic adding machine and fibred Julia sets, Stochastic and Dynamics, 13 (2013), 1250021, 26pp.
doi: 10.1142/S0219493712500219. |
[14] |
R. A. Uceda, Máquina de Somar, Conjuntos de Julia e Fractais de Rauzy, PhD Thesis, 2011. |
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