منابع مشابه
The Pentagram Map
Work supported by an Alfred P. Sloan Doctoral Dissertation Fellowship. We consider the pentagram map on the space of plane convex pentagons obtained by drawing a pentagon’s diagonals, recovering unpublished results of Conway and proving new ones. We generalize this to a ‘‘pentagram map’’ on convex polygons of more than five sides, showing that iterated images of any initial polygon converge exp...
متن کاملThe Pentagram Map is Recurrent
CONTENTS The pentagram map is defined on the space of convex n-gons
متن کاملOn Integrable Generalizations of the Pentagram Map
In this paper we prove that the generalization to RP of the pentagram map defined in [4] is invariant under certain scalings for any n. This property allows the definition of a Lax representation for the map, to be used to establish its integrability.
متن کاملThe pentagram map: A discrete integrable system
The pentagram map is a projectively natural transformation defined on (twisted) polygons. A twisted polygon is a map from Z into RP that is periodic modulo a projective transformation called the monodromy. We find a Poisson structure on the space of twisted polygons and show that the pentagram map relative to this Poisson structure is completely integrable. For certain families of twisted polyg...
متن کاملOn singularity confinement for the pentagram map
The pentagram map, introduced by R. Schwartz, is a birational map on the configuration space of polygons in the projective plane. We study the singularities of the iterates of the pentagram map. We show that a “typical” singularity disappears after a finite number of iterations, a confinement phenomenon first discovered by Schwartz. We provide a method to bypass such a singular patch by directl...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2015
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2014.07.003