79 citations · 1k across the 43 of their papers we have counts for
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Accurate predictions of chaotic motion of a free fall disk
Tianzhuang Xu, Jing Li, Zhihui Li +1
It is important to know the accurate trajectory of a free fall object in fluid (such as a spacecraft), whose motion might be chaotic in many cases. However, it is impossible to acc…
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…
On the risks of using double precision in numerical simulations of spatio-temporal chaos
Tianli Hu, Shijun Liao
Due to the butterfly-effect, computer-generated chaotic simulations often deviate exponentially from the true solution, so that it is very hard to obtain a reliable simulation of c…
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…
Influence of round-off errors on the reliability of numerical simulations of chaotic dynamic systems
Shijie Qin, Shijun Liao
We illustrate that, like the truncation error, the round-off error has a significant influence on the reliability of numerical simulations of chaotic dynamic systems. Due to the bu…
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…
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 comment on the arguments about the reliability and convergence of chaotic simulations
Shijun Liao
Yao and Hughes commented (Tellus-A, 60: 803 - 805, 2008) that "all chaotic responses are simply numerical noise and have nothing to do with the solutions of differential equations"…
Physical limit of prediction for chaotic motion of three-body problem
Shijun Liao
A half century ago, Lorenz found the "butterfly effect" of chaotic dynamic systems and made his famous claim that long-term prediction of chaos is impossible. However, the meaning…
On the mathematically reliable long-term simulation of chaos of Lorenz equation in the interval [0,10000]
Shijun Liao, Pengfei Wang
Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data, we have…
Chaotic motion of three-body problem : an origin of macroscopic randomness of the universe
Shijun Liao
The famous three-body problem is investigated by means of a numerical approach with negligible numerical noises in a long enough time interval, namely the Clean Numerical Simulatio…
On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems
S. J. Liao
In this paper, an extremely accurate numerical algorithm, namely the "clean numerical simulation" (CNS), is proposed to accurately simulate the propagation of micro-level inherent…
Chaos: a bridge from microscopic uncertainty to macroscopic randomness
S. J. Liao
It is traditionally believed that the macroscopic randomness has nothing to do with the micro-level uncertainty. Besides, the sensitive dependence on initial condition (SDIC) of Lo…
On the reliability of computed chaotic solutions of nonlinear differential equations
Shijun Liao
In this paper a new concept, namely the critical predictable time , is introduced to give a more precise description of computed chaotic solutions of nonlinear differential eq…