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The $\beta$-transformation with a hole
1. | School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom |
References:
[1] |
P. Boyland, A. de Carvalho and T. Hall, On digit frequencies in $\beta$-expansions,, Transactions of the AMS, (). Google Scholar |
[2] |
S. Bullett and P. Sentenac, Ordered orbits of the shift, square roots, and the devil's staircase,, Math. Proc. Camb. Phil. Soc., 115 (1994), 451.
doi: 10.1017/S0305004100072236. |
[3] |
P. Glendinning and N. Sidorov, The doubling map with asymmetrical holes,, Ergodic Theory and Dynamical Systems, 35 (2015), 1208.
doi: 10.1017/etds.2013.98. |
[4] |
P. Glendinning and C. T. Sparrow, Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps,, Physica D, 62 (1993), 22.
doi: 10.1016/0167-2789(93)90270-B. |
[5] |
L. Goldberg and C. Tresser, Rotation and the Farey tree,, Ergodic Theory and Dynamical Systems, 16 (1996), 1011.
doi: 10.1017/S0143385700010154. |
[6] |
K. G. Hare and N. Sidorov, On cycles for the doubling map which are disjoint from an interval,, Monatsh. Math., 175 (2014), 347.
doi: 10.1007/s00605-014-0646-y. |
[7] |
J. H. Hubbard and C. T. Sparrow, The classification of topologically expansive Lorenz maps,, Comm. Pure Appl. Math., 43 (1990), 431.
doi: 10.1002/cpa.3160430402. |
[8] |
M. Lothaire, Algebraic Combinatorics on Words,, Encyclopedia of Mathematics and its Applications, (2002).
doi: 10.1017/CBO9781107326019. |
[9] |
W. Parry, On the $\beta$-expansions of real numbers,, Acta Math. Acad. Sci. Hung., 11 (1960), 401.
doi: 10.1007/BF02020954. |
[10] |
A. Rényi, Representations for real numbers and their ergodic properties,, Acta Math. Acad. Sci. Hung., 8 (1957), 477.
doi: 10.1007/BF02020331. |
[11] |
N. Sidorov, Supercritical holes for the doubling map,, Acta Mathematica Hungarica, 143 (2014), 298.
doi: 10.1007/s10474-014-0403-7. |
[12] |
L. Vuillon, Balanced words,, Bull. Belg. Math. Soc. Simon Stevin, 10 (2003), 787.
|
show all references
References:
[1] |
P. Boyland, A. de Carvalho and T. Hall, On digit frequencies in $\beta$-expansions,, Transactions of the AMS, (). Google Scholar |
[2] |
S. Bullett and P. Sentenac, Ordered orbits of the shift, square roots, and the devil's staircase,, Math. Proc. Camb. Phil. Soc., 115 (1994), 451.
doi: 10.1017/S0305004100072236. |
[3] |
P. Glendinning and N. Sidorov, The doubling map with asymmetrical holes,, Ergodic Theory and Dynamical Systems, 35 (2015), 1208.
doi: 10.1017/etds.2013.98. |
[4] |
P. Glendinning and C. T. Sparrow, Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps,, Physica D, 62 (1993), 22.
doi: 10.1016/0167-2789(93)90270-B. |
[5] |
L. Goldberg and C. Tresser, Rotation and the Farey tree,, Ergodic Theory and Dynamical Systems, 16 (1996), 1011.
doi: 10.1017/S0143385700010154. |
[6] |
K. G. Hare and N. Sidorov, On cycles for the doubling map which are disjoint from an interval,, Monatsh. Math., 175 (2014), 347.
doi: 10.1007/s00605-014-0646-y. |
[7] |
J. H. Hubbard and C. T. Sparrow, The classification of topologically expansive Lorenz maps,, Comm. Pure Appl. Math., 43 (1990), 431.
doi: 10.1002/cpa.3160430402. |
[8] |
M. Lothaire, Algebraic Combinatorics on Words,, Encyclopedia of Mathematics and its Applications, (2002).
doi: 10.1017/CBO9781107326019. |
[9] |
W. Parry, On the $\beta$-expansions of real numbers,, Acta Math. Acad. Sci. Hung., 11 (1960), 401.
doi: 10.1007/BF02020954. |
[10] |
A. Rényi, Representations for real numbers and their ergodic properties,, Acta Math. Acad. Sci. Hung., 8 (1957), 477.
doi: 10.1007/BF02020331. |
[11] |
N. Sidorov, Supercritical holes for the doubling map,, Acta Mathematica Hungarica, 143 (2014), 298.
doi: 10.1007/s10474-014-0403-7. |
[12] |
L. Vuillon, Balanced words,, Bull. Belg. Math. Soc. Simon Stevin, 10 (2003), 787.
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