6 papers
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…
Statistical regularity and linear response of Mather measures for Tonelli Lagrangian systems
Alfonso Sorrentino, Jianlu Zhang, Siyao Zhu
We study the statistical regularity of Mather measures associated with perturbations of a Tonelli Lagrangian. When the unperturbed Mather measure is supported on a quasi-peri…
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 Au…
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…