The exponential map at a cuspidal singularity

EXPONENTIAL MAP OF A CLASS OF TOP SPACES

On 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...

exponential map of a class of top spaces

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A Reinjected Cuspidal Horseshoe

Horseshoes play a central role in dynamical systems and are observed in many chaotic systems. However most points in a neighborhood of the horseshoe escape after finite iterations. In this work we construct a model that possesses an attracting set that contains a cuspidal horseshoe with positive entropy. This model is obtained by reinjecting the points that escape the horseshoe and can be reali...

Invariant Subspaces and the Exponential Map

Bounded operators with no non-trivial closed invariant subspace have been constructed by P. Enflo [6]. In fact, there exist bounded operators on the space 1 with no non-trivial closed invariant subset [12]. It is still unknown, however, if such operators exist on reflexive Banach spaces, or on the separable Hilbert space. The main result of this note (Theorem 1) asserts that the existence of an...