Duanzhi Zhang

activity

20092023

most citedOn the number of P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in

R^{2 n}

8 citations · 20 across the 8 of their papers we have counts for

collaborators

8 papers

math.DS2023

Infinitely many Brake orbits of Tonelli Hamiltonian systems on the cotangent bundle

Duanzhi Zhang, Zhihao Zhao

We prove that on the twisted cotangent bundle of a closed manifold with an exact magnetic form, a Hamiltonian system of a time-dependent Tonelli Hamiltonian function possesses infi…

math.DS2019

Elliptic and non-hyperbolic closed characteristics on compact convex P-cyclic symmetric hypersurfaces in $R^{2 n}$

Hui Liu, Chongzhi Wang, Duanzhi Zhang

Let $Σ$ be a compact convex hypersurface in $R^{2 n}$ which is P-cyclic symmetric, i.e., $x \in Σ$ implies $P x \in Σ$ with P being a $2 n \times 2 n$ symplectic orthogonal matrix and…

math.DS2015

Stable P-symmetric closed characteristics on partially symmetric compact convex hypersurfaces

Hui Liu, Duanzhi Zhang

In this paper, let $n \geq 2$ be an integer, $P = d ia g (- I_{n - κ}, I_{κ}, - I_{n - κ}, I_{κ})$ for some integer $κ \in [0, n - 1)$ , and $Σ \subset R^{2 n}$ be a partially symmetric compact convex…

math.DS2014★ 8 cited

On the number of P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in $R^{2 n}$

Hui Liu, Duanzhi Zhang

In this paper, let $n \geq 2$ be an integer, $P = d ia g (- I_{n - κ}, I_{κ}, - I_{n - κ}, I_{κ})$ for some integer $κ \in [0, n)$ , and $Σ \subset R^{2 n}$ be a partially symmetric compact convex hy…

math.DS2013★ 1 cited

Seifert conjecture in the even convex case

Chungen Liu, Duanzhi Zhang

In this paper, we prove that there exist at least $n$ geometrically distinct brake orbits on every $C^{2}$ compact convex symmetric hypersurface $\Sg$ in $R^{2 n}$ satisfying the rev…

math.DS2011★ 4 cited

Multiple brake orbits on compact convex symmetric reversible hypersurfaces in $R^{2 n}$

Duanzhi Zhang, Chungen Liu

In this paper, we prove that there exist at least $[\frac{n + 1}{2}] + 1$ geometrically distinct brake orbits on every $C^{2}$ compact convex symmetric hypersurface $\Sg$ in $R^{2 n}$ fo…

math.DS2011★ 1 cited

Minimal period problems for brake orbits of nonlinear autonomous reversible semipositive Hamiltonian systems

Duanzhi Zhang

In this paper, for any positive integer $n$ , we study the Maslov-type index theory of $i_{L_{0}}$ , $i_{L_{1}}$ and $i_{- 1}^{L_{0}}$ with $L_{0} = {0} \times R^{n} \subset R^{2 n}$ and…

math.SG2009★ 6 cited

Iteration theory of $L$ -index and Multiplicity of brake orbits

Chungen Liu, Duanzhi Zhang

In this paper, we first establish the Bott-type iteration formulas and some abstract precise iteration formulas of the Maslov-type index theory associated with a Lagrangian subspac…

Infinitely many Brake orbits of Tonelli Hamiltonian systems on the cotangent bundle

Elliptic and non-hyperbolic closed characteristics on compact convex P-cyclic symmetric hypersurfaces in R2n