arXiv subjects

Huynh M. Hien

Publications and source records attributed to Huynh M. Hien.

3 recordsLinked to original sources

arXiv2023

Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex

This work deals with a maximal monotone operator $A$ of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value $Ax$ at a given point $x$ via its values at nearby points of $x$. We show that the faces of $Ax$ are contained in the set of all weak$^*$ convergent limits of bounded nets of the operator at nearby points of $x$, then we obtain a representation for $Ax$ by use of this set. In addition, representations for the support function of $Ax$ based on the minimal-norm selection of the operator in certain Banach spaces are given.

math.FA↗

arXiv2022

Markov partitions for the geodesic flow on compact Riemann surfaces of constant negative curvature

It is well-known that hyperbolic flows admit Markov partitions of arbitrarily small size. However, the constructions of Markov partitions for general hyperbolic flows are very abstract and not easy to understand. To establish a more detailed understanding of Markov partitions, in this paper we consider the geodesic flow on Riemann surfaces of constant negative curvature. We provide a rigorous construction of Markov partitions for this hyperbolic flow with explicit forms of rectangles and local cross sections. The local product structure is also calculated in detail.

math.DG↗

arXiv2022

Spectral form factor in the Hadamard-Gutzwiller model: orbit pairs contributing in the third order

In this paper we consider orbit pairs contributing in the third order of the spectral form factor in the Hadamard-Gutzwiller model. We prove that periodic orbits including two 2-encounters in certain structures have partner orbits. The action differences are estimated at $\ln(1+u_1s_1)(1+u_2s_2)$ with explicit error bounds, where $(u_1,s_1)$ and $(u_2,s_2)$ are the coordinates of the piercing points. A new symbolic dynamics for orbit pairs via conjugacy classes is also provided.

math-ph↗