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...
| Autores: | , , , |
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| 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 |
| 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 |
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