43 citations · 169 across the 15 of their papers we have counts for
16 papers
Analytic Liouville Integrable Geodesic Flow Has Zero Entropy
Fei Liu, Xiaokai Liu, Xiang Zhang
This paper studies the topological entropy of real-analytic Liouville integrable Hamiltonian systems. We prove that the Hamiltonian flow on a compact connected regular energy hyper…
Meromorphic first integrals of analytic diffeomorphisms
Antoni Ferragut, Armengol Gasull, Xiang Zhang
We give an upper bound for the number of functionally independent meromorphic first integrals that a discrete dynamical system generated by an analytic map can have in a neighb…
Regularity and convergence of local first integrals of analytic differential systems
Xiang Zhang
Poincaré proved nonexistence of formal first integrals near a nonresonant singularity of analytic autonomous differential systems. In the resonant case with one zero eigenvalue and…
Centralizers and normalizers of local analytic and formal vector fields
Niclas Kruff, Sebastian Walcher, Xiang Zhang
We investigate the structure of the centralizer and the normalizer of a local analytic or formal differential system at a nondegenerate stationary point, using the theory of Poinca…
A note on local integrability of differential systems
Xiang Zhang
For an --dimensional local analytic differential system with , the Poincaré nonintegrability theorem states that if the eigenvalues of are no…
Global dynamics of planar quasi-homogeneous differential systems
Yilei Tang, Xiang Zhang
In this paper we provide a new method to study global dynamics of planar quasi--homogeneous differential systems. We first prove that all planar quasi--homogeneous polynomial diffe…
The number of polynomial solutions of polynomial Riccati equations
Armengol Gasull, Joan Torregrosa, Xiang Zhang
Consider real or complex polynomial Riccati differential equations with all the involved functions being polynomials of degree at most . W…
Generalized rational first integrals of analytic differential systems
Wang Cong, Jaume Llibre, Xiang Zhang
In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the r…
The th Hilbert problem on algebraic limit cycles
Zhang Xiang
For real planar polynomial differential systems there appeared a simple version of the th Hilbert problem on algebraic limit cycles: {\it Is there an upper bound on the number…
Analytic integrable systems: Analytic normalization and embedding flows
Zhang Xiang
In this paper we mainly study the existence of analytic normalization and the normal form of finite dimensional complete analytic integrable dynamical systems. More details, we wil…
Analytic normalization of analytically integrable differential systems near a periodic orbit
Kesheng Wu, Xiang Zhang
For an analytic differential system in with a periodic orbit, we will prove that if the system is analytically integrable around the periodic orbit, i.e. it has …
Inverse Jacobian multipliers and Hopf bifurcation on center manifolds
Xiang Zhang
In this paper we consider a class of higher dimensional differential systems in which have a two dimensional center manifold at the origin with a pair of pure imagina…
Global structure of quaternion polynomial differential equations
Xiang Zhang
In this paper we mainly study the global structure of the quaternion Bernoulli equations for the quaternion field and also some other form of cubi…
Nonuniform Dichotomy Spectrum and Normal Forms for Nonautonomous Differential Systems
Xiang Zhang
The aim of this paper is to study the normal forms of nonautonomous differential systems. For doing so, we first investigate the nonuniform dichotomy spectrum of the linear evoluti…
Liouvillian integrability of polynomial differential systems
Xiang Zhang
M.F. Singer [Liouvillian first integrals of differential equations, Trans. Amer. Math. Soc. 333 (1992), 673--688] proved the equivalence between Liouvillian integrability and Darbo…
Sharp global regularity for the 2+1-dimensional equivariant Faddeev model
Dan-Andrei Geba, Kenji Nakanishi, Xiang Zhang
The aim of this article is to prove that for the 2+1-dimensional equivariant Faddeev model, which is a quasilinear generalization of the corresponding nonlinear sigma model, small…