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Pointwise periodic maps with quantized first integrals

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Titel: Pointwise periodic maps with quantized first integrals
Autoren: Gasull, Armengol, Cima, Anna, Mañosa Fernández, Víctor, Mañosas, Francesc
Weitere Verfasser: Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions
Publikationsjahr: 2020
Bestand: Universitat Politècnica de Catalunya, BarcelonaTech: UPCommons - Global access to UPC knowledge
Schlagwörter: Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals, Difference equations, Differentiable dynamical systems, Discrete geometry, Periodic points, Pointwise periodic maps, Piecewise linear maps, Quantized first integrals, Regular tessellations, Equacions en diferències, Sistemes dinàmics diferenciables, Geometria discreta, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems, Classificació AMS::39 Difference and functional equations::39A Difference equations, Classificació AMS::52 Convex and discrete geometry::52C Discrete geometry
Beschreibung: Preprint ; In a series of papers, Chang, Cheng and Wang studied the periodic behavior of some piecewise linear maps in the plane. These examples are valuable under the light of the classical result of Montgomery about periodic homeomorphisms, since they are pointwise periodic but not periodic. We revisit them from the point of view of their properties as integrable systems. We describe their global dynamics in terms of the dynamics induced by the maps on the level sets of certain first integrals that we also find. We believe that some of the features that the first integrals exhibit are interesting by themselves, for instance the set of values of the integrals are discrete. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of some prescribed tiles of certain regular tessellations. The existence of these quantized integrals is quite novel in the context of discrete dynamic systems theory. ; The third author acknowledges the group’s research recognition 2017-SGR-388 from AGAUR, Generalitat de Catalunya ; Preprint
Publikationsart: report
Dateibeschreibung: 43 p.; application/pdf
Sprache: English
Relation: arXiv:2010.12901 [math.DS]; https://arxiv.org/abs/2010.12901; info:eu-repo/grantAgreement/MINECO/1PE/DPI2016-77407-P; Gasull, A. [et al.]. Pointwise periodic maps with quantized first integrals. 2020.; http://hdl.handle.net/2117/332940
Verfügbarkeit: http://hdl.handle.net/2117/332940
Rights: Open Access
Dokumentencode: edsbas.52C2BD9E
Datenbank: BASE
Beschreibung
Abstract:Preprint ; In a series of papers, Chang, Cheng and Wang studied the periodic behavior of some piecewise linear maps in the plane. These examples are valuable under the light of the classical result of Montgomery about periodic homeomorphisms, since they are pointwise periodic but not periodic. We revisit them from the point of view of their properties as integrable systems. We describe their global dynamics in terms of the dynamics induced by the maps on the level sets of certain first integrals that we also find. We believe that some of the features that the first integrals exhibit are interesting by themselves, for instance the set of values of the integrals are discrete. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of some prescribed tiles of certain regular tessellations. The existence of these quantized integrals is quite novel in the context of discrete dynamic systems theory. ; The third author acknowledges the group’s research recognition 2017-SGR-388 from AGAUR, Generalitat de Catalunya ; Preprint