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december 2018 Periodic orbits of the three dimensional logarithm galactic potential
Daniel Paşca, Bogdan Mircea Tătaru
Bull. Belg. Math. Soc. Simon Stevin 25(4): 611-627 (december 2018). DOI: 10.36045/bbms/1546570913

Abstract

We apply the averaging theory of first order to study analytically families of periodic orbits for a three dimensional logarithmic galactic potential $H=\dfrac12 (p_x^2+p_y^2+p_z^2) + \dfrac{ v_0^2}{2} \ln(x^2 - \lambda x^3 + \alpha y^2+b z^2 + c_b^2)$, that is relevant in the study of elliptic galactic dynamics. We first introduce a scale transformation in the coordinates and momenta with a parameter $\varepsilon$ and we find, using averaging theory of first order in $\varepsilon$, the existence up to three periodic orbits if $\alpha,\beta$ are irrational, and one periodic orbit if either $\alpha$ is irrational and $\beta$ is rational, or $\beta$ is irrational and $\alpha$ is rational, for $\varepsilon$ sufficiently small.

Citation

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Daniel Paşca. Bogdan Mircea Tătaru. "Periodic orbits of the three dimensional logarithm galactic potential." Bull. Belg. Math. Soc. Simon Stevin 25 (4) 611 - 627, december 2018. https://doi.org/10.36045/bbms/1546570913

Information

Published: december 2018
First available in Project Euclid: 4 January 2019

zbMATH: 07038172
MathSciNet: MR3896275
Digital Object Identifier: 10.36045/bbms/1546570913

Subjects:
Primary: 34C10, 34C25

Rights: Copyright © 2018 The Belgian Mathematical Society

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Vol.25 • No. 4 • december 2018
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