Downloads provided by UsageCountsPointwise periodic maps with quantized first integrals
Copyright policy ) Anna Cima; Armengol Gasull; Víctor Mañosa; Francesc Mañosas;
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 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.
46 pages, 20 figures
Difference equations, Integrable difference and lattice equations; integrability tests, Quantized first integrals, regular and uniform tessellations, periodic points, Periodic and quasi-periodic flows and diffeomorphisms, Classificació AMS::39 Difference and functional equations::39A Difference equations, Dynamical Systems (math.DS), Geometria discreta, Tilings in \(2\) dimensions (aspects of discrete geometry), :Matemàtiques i estadística::Equacions diferencials i integrals [Àrees temàtiques de la UPC], Equacions en diferències, Periodic points, pointwise periodic maps, Completely integrable discrete dynamical systems, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], FOS: Mathematics, Differentiable dynamical systems, and nonholonomic systems, Mathematics - Dynamical Systems, Periodic solutions of difference equations, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems, Lagrangian, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals, Classificació AMS::52 Convex and discrete geometry::52C Discrete geometry, Discrete geometry, :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 [Classificació AMS], Sistemes dinàmics diferenciables, quantized first integrals, Regular and uniform tessellations, Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, Primary: 37C25, 39A23. Secondary: 37C55, 37J35, 52C20, Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Piecewise linear maps, piecewise linear maps, Pointwise periodic maps, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, contact
Difference equations, Integrable difference and lattice equations; integrability tests, Quantized first integrals, regular and uniform tessellations, periodic points, Periodic and quasi-periodic flows and diffeomorphisms, Classificació AMS::39 Difference and functional equations::39A Difference equations, Dynamical Systems (math.DS), Geometria discreta, Tilings in \(2\) dimensions (aspects of discrete geometry), :Matemàtiques i estadística::Equacions diferencials i integrals [Àrees temàtiques de la UPC], Equacions en diferències, Periodic points, pointwise periodic maps, Completely integrable discrete dynamical systems, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], FOS: Mathematics, Differentiable dynamical systems, and nonholonomic systems, Mathematics - Dynamical Systems, Periodic solutions of difference equations, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems, Lagrangian, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals, Classificació AMS::52 Convex and discrete geometry::52C Discrete geometry, Discrete geometry, :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 [Classificació AMS], Sistemes dinàmics diferenciables, quantized first integrals, Regular and uniform tessellations, Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, Primary: 37C25, 39A23. Secondary: 37C55, 37J35, 52C20, Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Piecewise linear maps, piecewise linear maps, Pointwise periodic maps, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, contact
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