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From greedy to lazy expansions and their driving dynamics |
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| Authors: | Karma Dajani Cor Kraaikamp |
| Institution: | 1Mathematics Department, Utrecht University, 3508 TA Utrecht, The Netherlands 2TU Delft, Department of Information Technology and Systems, CROSS, Thomas Stieltjes Institute for Mathematics, Mekelweg 4, 2628 CD Delft, The Netherlands |
| Abstract: | In this paper we study the ergodic properties of non-greedy series expansions to non-integer bases β > 1. It is shown that the so-called ‘lazy’ expansion is isomorphic to the ‘greedy’ expansion. Furthermore, a class of expansions to base β > 1, β   , ‘in between’ the lazy and the greedy expansions are introduced and studies. It is shown that these expansions are isomorphic to expansions of the form Tx = βx +  (mod 1). |
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