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Open AccessArticle

About the Orbit Structure of Sequences of Maps of Integers

1
Department of Mathematics, West Chester University of Pennsylvania, West Chester, PA 19383, USA
2
Institute of Mathematics, Romanian Academy P.O. Box 1764, RO-70700 Bucharest, Romania
3
Department of Mathematics, Ramnarain Ruia Autonomous College, L. Napoo Rd, Matunga, Mumbai, Maharashtra 4000019, India
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(11), 1374; https://doi.org/10.3390/sym11111374
Received: 9 August 2019 / Revised: 27 September 2019 / Accepted: 30 September 2019 / Published: 6 November 2019
(This article belongs to the Special Issue Symmetry and Dynamical Systems)
Motivated by connections to the study of sequences of integers, we study, from a dynamical systems point of view, the orbit structure for certain sequences of maps of integers. We find sequences of maps for which all individual orbits are bounded and periodic and for which the number of periodic orbits of fixed period is finite. This allows the introduction of a formal ζ -function for the maps in these sequences, which are actually polynomials. We also find sequences of maps for which the orbit structure is more complicated, as they have both bounded and unbounded orbits, both individual and global. Most of our results are valid in a general numeration base. View Full-Text
Keywords: orbit structure; bounded orbit; unbounded orbit; bARH-number; bMRH-number; bw-ARH-number; bwMRH-number; sdditive multiplier; multiplicative multiplier; additive extra term; multiplicative extra term; fixed point, sequence of integers; sequence of maps of integers orbit structure; bounded orbit; unbounded orbit; bARH-number; bMRH-number; bw-ARH-number; bwMRH-number; sdditive multiplier; multiplicative multiplier; additive extra term; multiplicative extra term; fixed point, sequence of integers; sequence of maps of integers
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Niţică, V.; Makhania, J. About the Orbit Structure of Sequences of Maps of Integers. Symmetry 2019, 11, 1374.

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