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Dynamics of $\lambda$-continued fractions and $\beta$-shifts
1. | Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, CNRS, Avenue de l’Université, 76801 Saint Étienne du Rouvray, France |
2. | Laboratoire Analyse, Géométrie et Applications, Université Paris 13 Institut Galilée, CNRS, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France |
3. | Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, CNRS, Avenue de l'Université, Avenue de l'Université, 76801 Saint Étienne du Rouvray, France |
References:
[1] |
F. Blanchard, $\beta$-expansions and symbolic dynamics, Theoret. Comput. Sci., 65 (1989), 131-141. |
[2] |
Karma Dajani and Martijn de Vries, Measures of maximal entropy for random $\beta$-expansions, J. Eur. Math. Soc. (JEMS), 7 (2005), 51-68. |
[3] |
Karma Dajani and Martijn de Vries, Invariant densities for random $\beta$-expansions, J. Eur. Math. Soc. (JEMS), 9 (2007), 157-176. |
[4] |
Shunji Ito and Yōichirō Takahashi, Markov subshifts and realization of $\beta $-expansions, J. Math. Soc. Japan, 26 (1974), 33-55.
doi: 10.2969/jmsj/02610033. |
[5] |
Élise Janvresse, Benoît Rittaud and Thierry de la Rue, How do random Fibonacci sequences grow?, Prob. Th. Rel. Fields, 142 (2008), 619-648.
doi: 10.1007/s00440-007-0117-7. |
[6] |
. Janvresse, B. Rittaud and T. de la Rue, Almost-sure growth rate of generalized random Fibonacci sequences, Ann. IHP, Probab. Stat., 46 (2010), 135-158.
doi: 10.1214/09-AIHP312. |
[7] |
W. Parry, On the $\beta $-expansions of real numbers, Acta Math. Acad. Sci. Hungar, 11 (1960), 401-416.
doi: 10.1007/BF02020954. |
[8] |
A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar, 8 (1957), 477-493.
doi: 10.1007/BF02020331. |
[9] |
David Rosen, A class of continued fractions associated with certain properly discontinuous groups, Duke Math. J., 21 (1954), 549-563.
doi: 10.1215/S0012-7094-54-02154-7. |
show all references
References:
[1] |
F. Blanchard, $\beta$-expansions and symbolic dynamics, Theoret. Comput. Sci., 65 (1989), 131-141. |
[2] |
Karma Dajani and Martijn de Vries, Measures of maximal entropy for random $\beta$-expansions, J. Eur. Math. Soc. (JEMS), 7 (2005), 51-68. |
[3] |
Karma Dajani and Martijn de Vries, Invariant densities for random $\beta$-expansions, J. Eur. Math. Soc. (JEMS), 9 (2007), 157-176. |
[4] |
Shunji Ito and Yōichirō Takahashi, Markov subshifts and realization of $\beta $-expansions, J. Math. Soc. Japan, 26 (1974), 33-55.
doi: 10.2969/jmsj/02610033. |
[5] |
Élise Janvresse, Benoît Rittaud and Thierry de la Rue, How do random Fibonacci sequences grow?, Prob. Th. Rel. Fields, 142 (2008), 619-648.
doi: 10.1007/s00440-007-0117-7. |
[6] |
. Janvresse, B. Rittaud and T. de la Rue, Almost-sure growth rate of generalized random Fibonacci sequences, Ann. IHP, Probab. Stat., 46 (2010), 135-158.
doi: 10.1214/09-AIHP312. |
[7] |
W. Parry, On the $\beta $-expansions of real numbers, Acta Math. Acad. Sci. Hungar, 11 (1960), 401-416.
doi: 10.1007/BF02020954. |
[8] |
A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar, 8 (1957), 477-493.
doi: 10.1007/BF02020331. |
[9] |
David Rosen, A class of continued fractions associated with certain properly discontinuous groups, Duke Math. J., 21 (1954), 549-563.
doi: 10.1215/S0012-7094-54-02154-7. |
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