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Student: Ben Stilin, Program in Applied Mathematics
Title: Scaling laws for small random perturbations of an intermittently chaotic system
Advisors: Kevin Lin, Math Department and Shankar Venkataramani, Math Department
Location: ENR2, Room S395 | Zoom link: https://arizona.zoom.us/j/84477414141
Abstract: We analyze the invariant densities of a randomly perturbed circle map with a neutral fixed point, using a symmetrized Pomeau--Manneville model with additive noise. The deterministic density has an integrable singularity at the fixed point, and the noisy densities are known to converge to the deterministic density in L^1 as the noise amplitude approaches zero. To characterize the structure of the noisy density and its convergence properties, we develop a formal matched asymptotic framework. By matching a stochastic differential equation approximation near the fixed point with the discrete dynamics in the chaotic region, our closed-form approximation reveals the boundary-layer profile and predicts explicit scaling laws for both the L^1-convergence rate and the spectral gap closure rate. These scaling predictions and profiles are confirmed numerically using a Galerkin method with nonuniform B-splines.