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Almost every interval translation map of three intervals is finite type
1. | Kungliga Tekniska Hogskolan (Royal Institute of Technology), Department of mathematics, SE-100 44, Stockholm, Sweden |
References:
[1] |
M. Boshernitzan and I. Kornfeld, Interval translation mappings, Ergodic Theory Dynam. Systems, 15 (1995), 821-832.
doi: 10.1017/S0143385700009652. |
[2] |
H. Bruin, Renormalization in a class of interval translation maps of $d$ branches, Dyn. Syst., 22 (2007), 11-24.
doi: 10.1080/14689360601028084. |
[3] |
H. Bruin and G. Clack, Inducing and unique ergodicity of double rotations, Discrete Contin. Dyn. Syst., 32 (2012), 4133-4147.
doi: 10.3934/dcds.2012.32.4133. |
[4] |
H. Bruin and S. Troubetzkoy, The Gauss map on a class of interval translation mappings, Israel J. Math., 137 (2003), 125-148.
doi: 10.1007/BF02785958. |
[5] |
J. Buzzi, Piecewise isometries have zero topological entropy, Ergodic Theory Dynam. Systems, 21 (2001), 1371-1377.
doi: 10.1017/S0143385701001651. |
[6] |
J. Buzzi and P. Hubert, Piecewise monotone maps without periodic points: Rigidity, measures and complexity, Ergodic Theory Dynam. Systems, 24 (2004), 383-405.
doi: 10.1017/S0143385703000488. |
[7] |
A. Goetz, Sofic subshifts and piecewise isometric systems, Ergodic Theory Dynam. Systems, 19 (1999), 1485-1501.
doi: 10.1017/S0143385799151964. |
[8] |
A. Goetz, Dynamics of piecewise isometries, Illinois J. Math., 44 (2000), 465-478. |
[9] |
A. Goetz, Stability of piecewise rotations and affine maps, Nonlinearity, 14 (2001), 205-219.
doi: 10.1088/0951-7715/14/2/302. |
[10] |
J. Schmeling and S. Troubetzkoy, Interval Translation Mappings, In Dynamical systems (Luminy-Marseille, 1998), 291-302. World Sci. Publ., River Edge, NJ, 2000. |
[11] |
H. Suzuki, S. Ito and K. Aihara, Double rotations, Discrete Contin. Dyn. Syst., 13 (2005), 515-532.
doi: 10.3934/dcds.2005.13.515. |
show all references
References:
[1] |
M. Boshernitzan and I. Kornfeld, Interval translation mappings, Ergodic Theory Dynam. Systems, 15 (1995), 821-832.
doi: 10.1017/S0143385700009652. |
[2] |
H. Bruin, Renormalization in a class of interval translation maps of $d$ branches, Dyn. Syst., 22 (2007), 11-24.
doi: 10.1080/14689360601028084. |
[3] |
H. Bruin and G. Clack, Inducing and unique ergodicity of double rotations, Discrete Contin. Dyn. Syst., 32 (2012), 4133-4147.
doi: 10.3934/dcds.2012.32.4133. |
[4] |
H. Bruin and S. Troubetzkoy, The Gauss map on a class of interval translation mappings, Israel J. Math., 137 (2003), 125-148.
doi: 10.1007/BF02785958. |
[5] |
J. Buzzi, Piecewise isometries have zero topological entropy, Ergodic Theory Dynam. Systems, 21 (2001), 1371-1377.
doi: 10.1017/S0143385701001651. |
[6] |
J. Buzzi and P. Hubert, Piecewise monotone maps without periodic points: Rigidity, measures and complexity, Ergodic Theory Dynam. Systems, 24 (2004), 383-405.
doi: 10.1017/S0143385703000488. |
[7] |
A. Goetz, Sofic subshifts and piecewise isometric systems, Ergodic Theory Dynam. Systems, 19 (1999), 1485-1501.
doi: 10.1017/S0143385799151964. |
[8] |
A. Goetz, Dynamics of piecewise isometries, Illinois J. Math., 44 (2000), 465-478. |
[9] |
A. Goetz, Stability of piecewise rotations and affine maps, Nonlinearity, 14 (2001), 205-219.
doi: 10.1088/0951-7715/14/2/302. |
[10] |
J. Schmeling and S. Troubetzkoy, Interval Translation Mappings, In Dynamical systems (Luminy-Marseille, 1998), 291-302. World Sci. Publ., River Edge, NJ, 2000. |
[11] |
H. Suzuki, S. Ito and K. Aihara, Double rotations, Discrete Contin. Dyn. Syst., 13 (2005), 515-532.
doi: 10.3934/dcds.2005.13.515. |
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