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Convergence Rate of Birkhoff Average for Toral Quasi-Periodic Rotations and Applications
Son N. T. Tu, Jianlu Zhang, Siyao Zhu
In this paper, we establish quantitative Denjoy--Koksma type estimates for higher-dimensional quasi-periodic torus rotations. For Diophantine frequency vectors, we establish quanti…
Quantitative homogenization for static contact Hamilton-Jacobi equations
Gengyu Liu, Son N. T. Tu, Jianlu Zhang
We characterize possible pairs addressing the homogenization problem for Hamilton…
Vanishing discount limits for first-order fully nonlinear Hamilton-Jacobi equations on noncompact domains
Son N. T. Tu, Jianlu Zhang
We study the asymptotic behavior of solutions to the fully nonlinear Hamilton-Jacobi equation in as . Under the assumption that the Aubr…
Polynomial Convergence Rate for Quasi-Periodic Homogenization of Hamilton-Jacobi Equations and Application to Ergodic Estimates
Bingyang Hu, Son N. T. Tu, Jianlu Zhang
In this paper, we demonstrate a polynomial convergence rate for homogenization of Hamilton-Jacobi equations with quasi-periodic potentials. We establish a connection between the co…
On the regularity of stochastic effective Hamiltonian
Son Tu, Jianlu Zhang
In this paper, we study the regularity of the ergodic constants for the viscous Hamilton--Jacobi equations. We also estimate the convergent rate of the ergodic constant in the vani…