Periodic orbits, superintegrability, and Bertrand's theorem

被引：2

作者：

Martinez-y-Romero, R. P. ^{[1
]}

Nunez-Yepez, H. N. ^{[2
]}

Salas-Brito, A. L. ^{[3
]}

机构：

[1] Univ Nacl Autonoma Mexico, Circuito Exterior, Fac Ciencias, Ciudad Univ, Mexico City 04510, DF, Mexico

[2] Univ Autonoma Metropolitana, Dept Fis, Unidad Iztapalapa, Apartado Postal 55-534, Mexico City 09340, DF, Mexico

[3] Univ Autonoma Metropolitana, Dept Ciencias Basicas, Lab Sistemas Dinam, Unidad Azcapotzalco, Apartado Postal 21-267, Mexico City 04000, DF, Mexico

来源：

AIP ADVANCES | 2020年 / 10卷 / 06期

关键词：

Hamiltonians;

D O I：

10.1063/1.5143582

中图分类号：

TB3 [工程材料学];

学科分类号：

0805 ; 080502 ;

摘要：

Periodic orbits are the key for understanding classical Hamiltonian systems. As we show here, they are the clue for understanding Bertrand's result relating the boundedness, flatness, and periodicity of orbits with the functional form of the potentials producing them. This result, which is known as Bertrand's theorem, was proved in 1883 using classical 19th century techniques. In this paper, we prove such a result using the relationship between the bounded plane and periodic orbits, constants of motion, and continuous symmetries in the Hamiltonian system.

引用

页数：5

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