Continuous limits of generalized pentagram maps

Y -meshes and generalized pentagram maps

We introduce a rich family of generalizations of the pentagram map sharing the property that each generates an infinite configuration of points and lines with four points on each line. These systems all have a description as Y -mutations in a cluster algebra and hence establish new connections between cluster theory and projective geometry. Résumé. Nous introduisons une famille de généralisatio...

R-semi-generalized Fuzzy Continuous Maps

In this paper, we introduce the concepts of r-semigeneralized fuzzy closed sets, r-semi-generalized fuzzy open sets, rsemi-generalized fuzzy continuous maps in fuzzy topological spaces and investigate some of their properties.

Generalized Covering Groups and Direct Limits

Integrable Cluster Dynamics of Directed Networks and Pentagram Maps

The pentagram map was introduced by R. Schwartz more than 20 years ago. In 2009, V. Ovsienko, R. Schwartz and S. Tabachnikov established Liouville complete integrability of this discrete dynamical system. In 2011, M. Glick interpreted the pentagram map as a sequence of cluster transformations associated with a special quiver. Using compatible Poisson structures in cluster algebras and Poisson g...

Higher pentagram maps, weighted directed networks, and cluster dynamics

The pentagram map was introduced by R. Schwartz about 20 years ago [25]. Recently, it has attracted a considerable attention: see [11, 16, 17, 20, 21, 22, 26, 27, 28, 29, 30] for various aspects of the pentagram map and related topics. On plane polygons, the pentagram map acts by drawing the diagonals that connect second-nearest vertices and forming a new polygon whose vertices are their consec...