Non-Autonomous Return Dynamics for Nested Convex Bodies:\\ Cubic Tangency, Summable Geometric Variation, and Critical Regimes

We study a non-autonomous geometric dynamics generated by successive normal transitions between nested convex boundaries sharing a common tangency point. For \(C_{k+1}\subset C_k\subset\mathbb{R}^2\), let \(\mathcal G_k:\partial C_k\to\partial C_{k+1}\) be the first intersection of the inward normal