58 citations · 67 across the 15 of their papers we have counts for
15 papers
Two Regularized Determinants of Laplacian through Resurgence theory
Wen Shen, Shanzhong Sun
We study two types of regularizations of the determinant of Laplacian on Riemann manifold from the viewpoint of resurgence theory. One is the formal logarithmic derivative of the d…
On the Uniqueness of Convex Central Configurations in the Planar -Body Problem
Shanzhong Sun, Zhifu Xie, Peng You
In this paper, we provide a rigorous computer-assisted proof (CAP) of the conjecture that there exists a unique convex central configuration for any four fixed positive masses in a…
Monodromy of Complexified Planar Kepler Problem
Shanzhong Sun, Peng You
The planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy.
A Weak -Functor in Morse Theory
Shanzhong Sun, Chenxi Wang
In the spirit of Morse homology initiated by Witten and Floer, we construct two -categories and . The weak one comes out of the Mor…
Resurgence and Partial Theta Series
Li Han, Yong Li, David Sauzin +1
We consider partial theta series associated with periodic sequences of coefficients, of the form , with non-negative integer and an …
Elliptic fixed points with an invariant foliation: Some facts and more questions
Alain Chenciner, David Sauzin, Shanzhong Sun +1
We address the following question: let F:(R^2,0)->(R^2,0) be an analytic local diffeomorphism defined in the neighborhood of the non resonant elliptic fixed point 0 and let Φbe a f…
On the Moyal Star Product of Resurgent Series
Yong Li, David Sauzin, Shanzhong Sun
We analyze the Moyal star product in deformation quantization from the resurgence theory perspective. By putting algebraic conditions on Borel transforms, one can define the space…
Hadamard Product and Resurgence Theory
Yong Li, David Sauzin, Shanzhong Sun
We discuss the analytic continuation of the Hadamard product of two holomorphic functions under assumptions pertaining to Ecalle's Resurgence Theory, proving that if both factors a…
The Baker-Campbell-Hausdorff formula via mould calculus
Shanzhong Sun, Yong Li, David Sauzin
The well-known Baker-Campbell-Hausdorff theorem in Lie theory says that the logarithm of a noncommutative product e X e Y can be expressed in terms of iterated commutators of X and…
Non-Embedding Theorems of Nilpotent Lie groups and Sub-Riemannian Manifolds
Yonghong Huang, Shanzhong Sun
We prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space…
Gutzwiller's Semiclassical Trace Formula and Maslov-Type Index Theory for Symplectic Paths
Shanzhong Sun
Gutzwiller's famous semiclassical trace formula plays an important role in theoretical and experimental quantum mechanics with tremendous success. We review the physical derivation…
A Double Poisson Algebra Structure on Fukaya Categories
Xiaojun Chen, Hai-Long Her, Shanzhong Sun +1
Let be an exact symplectic manifold with . Denote by the Fukaya category of . We show that the dual space of the bar construction of $\mathrm{Fuk…
Linear stability of elliptic Lagrangian solutions of the planar three-body problem via index theory
Xijun Hu, Yiming Long, Shanzhong Sun
It is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass paramete…
Cyclic Homology of Fukaya Categories and the Linearized Contact Homology
Xiaojun Chen, Hai-Long Her, Shanzhong Sun
Let be an exact symplectic manifold with contact type boundary such that . In this paper we show that the cyclic cohomology of the Fukaya category of has the stru…
Symmetry of Planar Four-Body Convex Central Configurations
Alain Albouy, Yanning Fu, Shanzhong Sun
We study the relationship between the masses and the geometric properties of central configurations. We prove that in the planar four-body problem, a convex central configuration i…