From the 1 of 6 linked papers with an AI index.
6 papers
Geometric Gradient Flows from Elliptic Level Sets: Normal Decomposition and Reflection Dynamics
Mohammed Barkatou, Mohamed El Morsalani
We investigate the asymptotic geometry of shifting superlevel sets generated by solutions to the elliptic Dirichlet problem in , wher…
Global Convergence of the Return Dynamics in the Class
Mohammed Barkatou, Mohamed El Morsalani
The paper studies a return map defined on domains with a fixed convex core, showing that its dynamics act like an adaptive gradient descent on the domain’s thickness function and c…
The Return Map in the Class : Geometry, Dynamics, and Thickness Regularity
Mohammed Barkatou, Mohamed El Morsalani
We investigate a geometric dynamical mechanism arising in the class of domains containing a fixed convex set and satisfying two geometric normals properties int…
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…
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…
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…