Papers - PENG Linyu

Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric

L Peng, H Sun, X Sun

International Journal of Mathematics and Mathematical Sciences 2011 ( 1 ) 710274 2011.09

Research paper (scientific journal), Joint Work, Accepted,  ISSN  01611712

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We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a family of conformal equivalent nondegenerate metrics are obtained. At last the conformal curvatures, the geodesic equations, the Jacobi equations, and the equations for the flow of the famous models, an N degrees of freedom linear Hamiltonian system and the Hénon-Heiles model are given, and in a special case, numerical solutions of the conformal geodesics, the generalized momenta, and the Jacobi field along the geodesics of the Hénon-Heiles model are obtained. And the numerical results for the Hénon-Heiles model show us the instability of the associated geodesic spreads. © 2011 Linyu Peng et al.

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The geometric structures and instability of entropic dynamical models

L Peng, H Sun, D Sun, J Yi

Advances in Mathematics (ELSEVIER)  227 ( 1 ) 459 - 471 2011.05

Research paper (scientific journal), Joint Work, Accepted,  ISSN  00018708

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In this paper, we characterize two entropic dynamical (ED) models from the viewpoint of information geometry and give the geometric structures of the associated statistical manifolds of the models. The scalar curvatures and the geodesics are obtained. Also the instability of entropic dynamical models is studied from the behavior of the geodesics lengths, statistical volume elements and Jacobi vector fields. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.

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Information geometry and its applications

Sun H, Peng L, Zhang Z

Advances in Mathematics (China) 40 ( 3 ) 257 - 269 2011

Research paper (scientific journal), Joint Work, Accepted

3D Object Recognition Based on Linear Lie Algebra Model

FX Li, PD Wu, HF Sun, LY Peng

Journal of Beijing Institute of Technology 18 ( 1 ) 46 - 50 2009.03

Research paper (scientific journal), Joint Work, Accepted,  ISSN  10040579

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A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed. Then an algorithm of 3D object recognition using the linear Lie algebra models is presented. It is a convenient recognition method for the objects which are symmetric about some axis. By using the presented algorithm, the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained. At last some recognition results of practicalities are given. © A paper published in JBIT is protected by copyright.

On Fibre Bundle Surfaces and Their Curvatures

FX Li, LY Peng, HF Sun

Journal of Beijing Institute of Technology 17 ( 4 ) 451 - 454 2008.12

Research paper (scientific journal), Joint Work, Accepted,  ISSN  10040579

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A surface model called the fibre bundle model is proposed. This model represents a surface locally as a direct product of two curves: a base curve and a fibre curve. We introduce the fibre bundle model and then obtain the Gaussian curvatures and the mean curvatures of a certain kind of fibre bundle surface models using 1-parameter groups of a linear Lie algebra as fibres. Some examples are given to verify our results.

The geometric structure of the inverse gamma distribution

T Li, L Peng, H Sun

Contributions to Algebra and Geometry 49 ( 1 ) 217 - 225 2008.04

Research paper (scientific journal), Joint Work, Accepted,  ISSN  01384821

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In the present paper we study the geometric structure of the inverse Gamma manifold from the viewpoint of information geometry and give the Kullback divergence, the J-divergence and the geodesic equations. Also, some applications of the inverse Gamma distribution are provided. © 2008 Heldermann Verlag.

Surface model based on a fibre bundle of Hamiltonian Lie algebra and Gaussian curvature

Li F, Wu P, Peng L, Sun H

Science & Technology Review 26 ( 8 ) 37 - 39 2008

Research paper (scientific journal), Joint Work, Accepted

The geometric structure of the Pareto distribution

L Peng, H Sun, L Jiu

Boletın de la Asociación Matemática Venezolana 14 ( 1-2 ) 5 - 13 2007

Research paper (scientific journal), Joint Work, Accepted