arXiv subjects

Zhijing Wendy Wang

Publications and source records attributed to Zhijing Wendy Wang.

6 recordsLinked to original sources

arXiv2026

Local Centralizer Rigidity near Elements of the Weyl Chamber Flow

In this paper, we prove centralizer rigidity near an element of the Weyl chamber flow on a semisimple Lie group. We show that a $C^1$ perturbation of an element of the Weyl chamber flow on a quotient $G/Γ$ of an $\R$-split, simple Lie group $G$ either has a centralizer of dimension $0$ or $1$, or is smoothly conjugate to an element of the Weyl chamber flow. We also obtain a general condition for the center-fixing centralizer of a partially hyperbolic diffeomorphism to be a Lie group.

math.DS↗

arXiv2026

Existence of a Hall ray in higher dimensional Lagrange spectra

Given any norm $\|\cdot\|_{\mathbb R^2}$ on $\mathbb R^2$, we prove that the Lagrange spectrum for $2$-vectors contains a Hall ray. Equivalently, every sufficiently small $ρ\ge0$ occurs as $\liminf_{q\to\infty}q^{1/2}\min_{p\in\mathbb Z^2}\|qx-p\|_{\mathbb R^2} $ for some $x\in\mathbb R^2\setminus\mathbb Q^2$. Combined with a recent result of Kleinbock \cite{Kleinbock}, this implies that the $2$-dimensional Lagrange spectrum is either a ray, mirroring the behavior for Dirichlet spectra, or a ray preceded by a dense part.

math.SP↗

arXiv2026

Local centralizer rigidity for a non-generic diagonal map

In this paper, we prove centralizer rigidity for any non-trivial diagonal map in the compact homogeneous space SL_n\mathbb{R}/Γ, n\ge 5, under the assumption that the perturbed volume-preserving diffeomorphism has a regular isomorphic centralizer.

math.DS↗

arXiv2026

Dynamics of composite symplectic Dehn twists

This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form of nonuniform hyperbolicity: it has positive topological entropy as well as two families of local stable and unstable Lagrangian manifolds, which are analogous to signatures of pseudo{-}Anosov mapping classes. Moreover, we show that the rank of the Floer cohomology group of these compositions grows exponentially under iterations, and provide a classification of the symplectic mapping class group of the $A^2_m$ configuration, which partially answers a question of Smith concerning the classification of symplectic mapping class group in higher dimensions. Finally, we propose a conjecture on the positive metric entropy of our model and point out its relationship with the standard map.

math.DS↗

arXiv2026

Local centralizer rigidity for twisted Weyl chamber flows

We prove local centralizer rigidity results for elements of Weyl chamber flows and twisted Weyl chamber flows on compact homogeneous spaces. For generic elements in the twisted setting, sufficiently large dimension of the centralizer forces smooth conjugacy to an algebraic model. For many non-generic elements, we prove analogous rigidity under a virtual centralizer-isomorphism hypothesis.

math.DS↗

arXiv2025

Complexity of Hofer's geometry in higher dimensional manifolds

This paper establishes robust obstructions to representing Hamiltonian diffeomorphisms as $k$-th powers ($k \geq 2$) or embedding them in flows for certain higher-dimensional symplectic manifolds $(M,ω)$, including surface bundles. We prove that in the Hamiltonian group $(\mathrm{Ham}(M,ω), d_H)$ equipped with the Hofer metric, there exist arbitrarily large balls that are disjoint from the set of $k$-th powers. Furthermore, we demonstrate that the free group on two generators embeds into every asymptotic cone of $(\mathrm{Ham}(M,ω), d_H)$, revealing the large-scale geometric complexity of the Hamiltonian group.

math.SG↗