Pointwise periodic maps with quantized first integrals

We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete, thus quantized. Furthermore, the level sets are bounded sets w...

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Detalles Bibliográficos
Autores: Cima, Anna, Gasull Embid, Armengol, Mañosa Fernández, Víctor|||0000-0002-5082-3334, Mañosas, Francesc
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/361708
Acceso en línea:https://hdl.handle.net/2117/361708
https://dx.doi.org/10.1016/j.cnsns.2021.106150
Access Level:acceso abierto
Palabra clave:Difference equations
Differentiable dynamical systems
Discrete geometry
Periodic points
Pointwise periodic maps
Piecewise linear maps
Quantized first integrals
Regular and uniform 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
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
Descripción
Sumario:We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete, thus quantized. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of open tiles of certain regular or uniform tessellations. The action of the maps on each invariant set of tiles is described geometrically