5 papers
Local stable and unstable sets for random dynamical systems
Xue Liu, Xiao Ma, Xiaomin Zhou
We study local stable and unstable sets for two-sided continuous bundle random dynamical systems with positive entropy. For two-sided continuous random dynamical systems and ergodi…
Long time derivation of the Boltzmann equation from hard sphere dynamics
Yu Deng, Zaher Hani, Xiao Ma
We provide a rigorous derivation of Boltzmann's kinetic equation from the hard sphere system for rarefied gas, which is valid for arbitrarily long times, as long as the solution to…
Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory
Yu Deng, Zaher Hani, Xiao Ma
In this paper, we rigorously derive the fundamental PDEs of fluid mechanics, such as the compressible Euler and incompressible Navier-Stokes-Fourier equations, starting from the ha…
Discrete spectrum of probability measures for locally compact group actions
Zongrui Hu, Xiao Ma, Leiye Xu +1
In this paper, we investigate the discrete spectrum of probability measures for actions of locally compact groups. We establish that a probability measure has a discrete spectrum i…
Invariant tori for a class of affined Anosov mappings with quasi-periodic forces
Xinyu Bai, Zeng Lian, Xiao Ma +1
In this paper, we consider a class of affined Anosov mappings with quasi-periodic forces, and show that there is a unique positive integer , which only depends on the system, su…