Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with non-specular reflection laws. We study the absolutely continuous invariant probabilities (acips) of the slap maps for several polygons, including regular polygons and triangles. We also present a general method for constructing polygons with slap maps with more than one ergodic acip.
Ergodicity of polygonal slap maps
Del Magno G.;
2014-01-01
Abstract
Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with non-specular reflection laws. We study the absolutely continuous invariant probabilities (acips) of the slap maps for several polygons, including regular polygons and triangles. We also present a general method for constructing polygons with slap maps with more than one ergodic acip.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
pre15.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
496.04 kB
Formato
Adobe PDF
|
496.04 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
