4 papers · 1 filter
Inverse Problems for the Return Map in the Class ( ): Reconstruction and Identifiability
Mohamed El Morsalani, Mohammed Barkatou
We study the inverse problem associated with the return map on the boundary of a convex core . By decomposing the return displacement into tangential and normal components,…
Non-Autonomous Return Dynamics for Nested Convex Bodies:\\ Cubic Tangency, Summable Geometric Variation, and Critical Regimes
Mohamed El Morsalani, Mohammed Barkatou
We study a non-autonomous geometric dynamics generated by successive normal transitions between nested convex boundaries sharing a common tangency point. For \(C_{k+1}\subset C_k\s…
Geometry, Dynamics, and Topology of the Thickness Landscape: A Morse-Theoretic Analysis of the Return Map in the Class
Mohammed Barkatou, Mohamed El Morsalani
We study the geometry, dynamics, and topology of the thickness landscape associated with the geometric return map in the class . For a convex core and an admissib…
Global Convergence Regimes of the Return Dynamics in the Class
Mohammed Barkatou, Mohamed El Morsalani
This study investigates the global dynamics of discrete return maps generated on the boundary of a convex core via an outwar…