On the Invertibility and Structural Properties of Interval Translation Maps
In this paper, we present a significant advancement by proving that each Interval Translation Map (ITM) is invertible almost everywhere on the support of its invariant measure. This result has far-reaching consequences, as it implies that ITMs reduce to Interval Exchange Maps (IEM) in some cases. Wh...
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| Published in | Lobachevskii journal of mathematics Vol. 46; no. 2; pp. 901 - 910 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.02.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1995-0802 1818-9962 |
| DOI | 10.1134/S1995080224606891 |
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| Abstract | In this paper, we present a significant advancement by proving that each Interval Translation Map (ITM) is invertible almost everywhere on the support of its invariant measure. This result has far-reaching consequences, as it implies that ITMs reduce to Interval Exchange Maps (IEM) in some cases. While previous work has noted that the support of the invariant measure may sometimes form a Cantor set, we are able to conclude that every ITM is indeed invertible almost everywhere on its support. This discovery extends the understanding of ITMs and their structural properties, providing a deeper insight into the behavior of these dynamical systems. Additionally, we investigate several properties of ITMs, contributing to a deeper understanding of their structural properties. |
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| AbstractList | In this paper, we present a significant advancement by proving that each Interval Translation Map (ITM) is invertible almost everywhere on the support of its invariant measure. This result has far-reaching consequences, as it implies that ITMs reduce to Interval Exchange Maps (IEM) in some cases. While previous work has noted that the support of the invariant measure may sometimes form a Cantor set, we are able to conclude that every ITM is indeed invertible almost everywhere on its support. This discovery extends the understanding of ITMs and their structural properties, providing a deeper insight into the behavior of these dynamical systems. Additionally, we investigate several properties of ITMs, contributing to a deeper understanding of their structural properties. |
| Author | Tajbakhsh, Khosro Yaghmaeian, Reza |
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| Cites_doi | 10.1007/BF02785958 10.1016/j.crma.2016.05.002 10.3934/dcds.2005.13.515 10.3390/axioms10020080 10.1051/mmnp/2019041 10.1017/S0143385703000488 10.1017/S0143385701001651 10.1007/978-1-4612-4190-4 10.1017/S0143385700009652 10.1080/14689360601028084 10.1016/j.physleta.2007.06.033 10.1017/S0143385799151964 10.3934/dcds.2014.34.2307 10.3934/dcds.2012.32.4133 10.1215/ijm/1256060408 |
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| Keywords | invertibility interval translation maps syndetic recurrence interval exchange maps 37E10 invariant measure 37A05 37E05 |
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| References | H. Bruin (8208_CR2) 2007; 22 A. Goetz (8208_CR9) 1999; 19 J. Buzzi (8208_CR6) 2004; 24 M. Boshernitzan (8208_CR1) 1995; 15 A. Katok (8208_CR11) 1997 H. Suzuki (8208_CR17) 2005; 13 H. Bruin (8208_CR4) 2003; 137 Z. Chen (8208_CR7) 2010; 14 8208_CR13 8208_CR12 H. Bruin (8208_CR3) 2012; 32 D. Volk (8208_CR19) 2014; 34 8208_CR21 8208_CR20 A. Goetz (8208_CR10) 2000; 44 X. Fu (8208_CR8) 2007; 37 S. Kryzhevich (8208_CR14) 2021; 10 B. Pires (8208_CR15) 2016; 354 8208_CR18 J. Buzzi (8208_CR5) 2001; 21 J. Schmeling (8208_CR16) 1998 |
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| Title | On the Invertibility and Structural Properties of Interval Translation Maps |
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