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A class of adding machines and Julia sets
1. | Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ, Brazil |
References:
[1] |
H. El Abdalaoui, S. Bonnot, A. Messaoudi and O. Sester, On the Fibonacci complex dynamical systems, Discrete and Continuous Dynamical Systems - A, 36 (2016), 2449-2471.
doi: 10.3934/dcds.2016.36.2449. |
[2] |
H. El Abdalaoui and A. Messaoudi, On the spectrum of stochastic perturbations of the shift and Julia Sets, Fundamenta Mathematicae, 218 (2012), 47-68.
doi: 10.4064/fm218-1-3. |
[3] |
D. A. Caprio, A class of adding machine and Julia sets, preprint, arXiv:1508.05062. |
[4] |
D. A. Caprio and A. Messaoudi, Julia Sets for a class of endomorphisms on $\mathbb{C}^2$, work in progress. |
[5] |
C. Frougny, Systṁes de numération linéaires et automates finis, Ph.D thesis, Université Paris 7, Rapport LITP 89-69, 1989. |
[6] |
C. Frougny, Fibonacci representations and finite automata, IEEE Trans. Inform. Theory, 37 (1991), 393-399.
doi: 10.1109/18.75263. |
[7] |
P. J. Grabner, P. Liardet and R. F. Tichy, Odometers and systems of numeration, Acta Arithmetica, 70 (1995), 103-123. |
[8] |
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. |
[9] |
P. R. Killeen and T. J. Taylor, How the propagation of error through stochastic counters affects time discrimination and other psychophysical judgements, Psychological Review, 107 (2000), 430-459. |
[10] |
G. F. Lawler, Introduction to Stochastic Processes, $1^{nd}$ edition, Chapman and Hall, 1995. |
[11] |
A. Messaoudi, O. Sester and G. Valle, Spectrum of stochastic adding machines and fibered Julia sets, Stochastics and Dynamics, 13 (2013), 1250021, 26 pages.
doi: 10.1142/S0219493712500219. |
[12] |
A. Messaoudi and D. Smania, Eigenvalues of Fibonacci stochastic adding machine, Stochastics and Dynamics, 10 (2010), 291-313.
doi: 10.1142/S0219493710002966. |
[13] |
A. Messaoudi and R. M. A. Uceda, Stochastic adding machine and 2-dimensional Julia sets, Discrete and Continuous Dynamical Systems - A, 34 (2014), 5247-5269.
doi: 10.3934/dcds.2014.34.5247. |
[14] |
A. Messaoudi and G. Valle, Spectra of stochastic adding machines based on Cantor Systems of Numeration, preprint, arXiv:1307.6876. |
[15] |
J. Milnor, Dynamics in one complex variable, $3^{nd}$ edition, Annals of Mathematics Studies, vol. 160, Princeton University Press, Princeton, NJ, 2006. |
[16] |
S. Morosawa, Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge Studies in Advanced Mathematics, vol. 66, Cambridge University Press, Cambridge, 2000. |
[17] | |
[18] |
E. Zeckendorff, Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Royale Sci. Liège, 42 (1972) 179-182. |
show all references
References:
[1] |
H. El Abdalaoui, S. Bonnot, A. Messaoudi and O. Sester, On the Fibonacci complex dynamical systems, Discrete and Continuous Dynamical Systems - A, 36 (2016), 2449-2471.
doi: 10.3934/dcds.2016.36.2449. |
[2] |
H. El Abdalaoui and A. Messaoudi, On the spectrum of stochastic perturbations of the shift and Julia Sets, Fundamenta Mathematicae, 218 (2012), 47-68.
doi: 10.4064/fm218-1-3. |
[3] |
D. A. Caprio, A class of adding machine and Julia sets, preprint, arXiv:1508.05062. |
[4] |
D. A. Caprio and A. Messaoudi, Julia Sets for a class of endomorphisms on $\mathbb{C}^2$, work in progress. |
[5] |
C. Frougny, Systṁes de numération linéaires et automates finis, Ph.D thesis, Université Paris 7, Rapport LITP 89-69, 1989. |
[6] |
C. Frougny, Fibonacci representations and finite automata, IEEE Trans. Inform. Theory, 37 (1991), 393-399.
doi: 10.1109/18.75263. |
[7] |
P. J. Grabner, P. Liardet and R. F. Tichy, Odometers and systems of numeration, Acta Arithmetica, 70 (1995), 103-123. |
[8] |
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. |
[9] |
P. R. Killeen and T. J. Taylor, How the propagation of error through stochastic counters affects time discrimination and other psychophysical judgements, Psychological Review, 107 (2000), 430-459. |
[10] |
G. F. Lawler, Introduction to Stochastic Processes, $1^{nd}$ edition, Chapman and Hall, 1995. |
[11] |
A. Messaoudi, O. Sester and G. Valle, Spectrum of stochastic adding machines and fibered Julia sets, Stochastics and Dynamics, 13 (2013), 1250021, 26 pages.
doi: 10.1142/S0219493712500219. |
[12] |
A. Messaoudi and D. Smania, Eigenvalues of Fibonacci stochastic adding machine, Stochastics and Dynamics, 10 (2010), 291-313.
doi: 10.1142/S0219493710002966. |
[13] |
A. Messaoudi and R. M. A. Uceda, Stochastic adding machine and 2-dimensional Julia sets, Discrete and Continuous Dynamical Systems - A, 34 (2014), 5247-5269.
doi: 10.3934/dcds.2014.34.5247. |
[14] |
A. Messaoudi and G. Valle, Spectra of stochastic adding machines based on Cantor Systems of Numeration, preprint, arXiv:1307.6876. |
[15] |
J. Milnor, Dynamics in one complex variable, $3^{nd}$ edition, Annals of Mathematics Studies, vol. 160, Princeton University Press, Princeton, NJ, 2006. |
[16] |
S. Morosawa, Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge Studies in Advanced Mathematics, vol. 66, Cambridge University Press, Cambridge, 2000. |
[17] | |
[18] |
E. Zeckendorff, Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Royale Sci. Liège, 42 (1972) 179-182. |
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