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Reachability in injective piecewise affine maps

Ghahremani, F ; Sharif University of Technology | 2023

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  1. Type of Document: Article
  2. DOI: 10.1109/LICS56636.2023.10175723
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2023
  4. Abstract:
  5. One of the most basic, longstanding open problems in the theory of dynamical systems is whether reachability is decidable for one-dimensional piecewise affine maps with two intervals. In this paper we prove that for injective maps, it is decidable.We also study various related problems, in each case either establishing decidability, or showing that they are closely connected to Diophantine properties of certain transcendental numbers, analogous to the positivity problem for linear recurrence sequences. Lastly, we consider topological properties of orbits of one-dimensional piecewise affine maps, not necessarily with two intervals, and negatively answer a question of Bournez, Kurganskyy, and Potapov, about the set of orbits in expanding maps. © 2023 IEEE
  6. Keywords:
  7. Computability and decidability ; Dynamical systems ; Expanding map ; Linear recurrences ; One-dimensional ; Piecewise affine maps ; Property ; Reachability ; Recurrence sequences ; Topological properties ; Topology
  8. Source: Proceedings - Symposium on Logic in Computer Science ; Volume 2023-June , 2023 ; 10436871 (ISSN); 979-835033587-3 (ISBN)
  9. URL: https://ieeexplore.ieee.org/document/10175723