56 citations · 245 across the 11 of their papers we have counts for
12 papers
Discovery of 10,059 new three-dimensional periodic orbits of general three-body problem
Xiaoming Li, Shijun Liao
A very few three-dimensional (3D) periodic orbits of general three-body problem (with three finite masses) have been discovered since Newton mentioned it in 1680s. Using a high-acc…
Three-body problem -- from Newton to supercomputer plus machine learning
Shijun Liao, Xiaoming Li, Yu Yang
The famous three-body problem can be traced back to Newton in 1687, but quite few families of periodic orbits were found in 300 years thereafter. In this paper, we propose an effec…
Satellites of the Broucke-Hadjidemetriou-Hénon family of periodic unequal-mass three-body orbits
Xiaoming Li, Shijun Liao
The Broucke-Hadjidemetriou-Hénon's (BHH) orbits are a family of periodic orbits of the three-body system with the simplest topological free group word , while the BHH satellites…
One family of 13315 stable periodic orbits of the non-hierarchical unequal-mass triple system
Xiaoming Li, Xiaochen Li, Shijun Liao
The three-body problem has been studied for more than three centuries [1,2], and has received much attention in recent years [3-5]. It shows complex dynamical phenomena due to the…
Collisionless periodic orbits in the free-fall three-body problem
Xiaoming Li, Shijun Liao
Although the free-fall three-body problem have been investigated for more than one century, however, only four collisionless periodic orbits have been found. In this paper, we repo…
The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum
Xiaoming Li, Yipeng Jing, Shijun Liao
We present 1349 families of Newtonian periodic planar three-body orbits with unequal mass and zero angular momentum and the initial conditions in case of isosceles collinear config…
More than six hundreds new families of Newtonian periodic planar collisionless three-body orbits
Xiaoming Li, Shijun Liao
The famous three-body problem can be traced back to Isaac Newton in 1680s. In the 300 years since this "three-body problem" was first recognized, only three families of periodic so…
The influence of numerical noises on statistics computation of chaotic dynamic systems
Xiaoming Li, Shijun Liao
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependance on initial conditions (SDIC). Unfortunately, numer…
Clean Numerical Simulation: A New Strategy to Obtain Reliable Solutions of Chaotic Dynamic Systems
Xiaoming Li, Shijun Liao
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependence on initial conditions (SDIC). Unfortunately, numer…
Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally
Xiaochen Li, Xiaoming Li, Shijun Liao
A system of two-dimensional, two coupled Faraday interfacial waves is experimentally observed at the two interfaces of the three layers of fluids (air, pure ethanol and silicon oil…
On the inherent self-excited macroscopic randomness of chaotic three-body system
Shijun Liao, Xiaoming Li
What is the origin of macroscopic randomness (uncertainty)? This is one of the most fundamental open questions for human being. In this paper, 10000 samples of reliable (convergent…
A commend on "Three Classes of Newtonian Three-Body Planar Periodic Orbits" by Šuvakov and Dmitrašinović (PRL, 2013)
Xiaoming Li, Shijun Liao
Currently, the fifteen new periodic solutions of Newtonian three-body problem with equal mass were reported by Šuvakov and Dmitrašinović (PRL, 2013) [1]. However, using a reliable…