3 papers
math.DS2026
Inverse Problems for the Return Map in the Class ( ): Reconstruction and Identifiability
Mohamed El Morsalani, Mohammed Barkatou
We analyze the inverse problem of recovering geometric information from the return map induced by a round-trip between a convex core C and an admissible domain. This process define…
math.DS2026
From Tangency to Fractals: Quadratic Dynamics in Nested Convex Geometry
Mohamed El Morsalani, Mohammed Barkatou
We study the dynamics generated by return maps associated with nested convex bodies and growing domains satisfying the geometric normal property in the plane. These maps are define…
math.DS2026
Geometry, Dynamics and Topology of Thickness Landscape: A Morse-Theoretic Analysis of the Return-Map in the Class
Mohammed Barkatou, Mohamed El Morsalani
We study the geometric and dynamical structure induced by the return map associated with domains in the class \(\mathcal{O}_{C}\). This map, defined through a geometric round-trip…