# A Birman-Schwinger Principle in Galactic DynamicsOn the Period Function T1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_1$$\end{document}

A Birman-Schwinger Principle in Galactic Dynamics: On the Period Function... [Associated with every effective potential, Ueff(r,ℓ)=UQ(r)+ℓ22r2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{\mathrm{eff}}(r, \ell )=U_Q(r)+\frac{\ell ^2}{2r^2}$$\end{document} is a period function T1(·,ℓ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_1(\cdot , \ell )$$\end{document} that is defined for certain energies e∈[emin(ℓ),e0]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e\in [e_{\mathrm{min}}(\ell ), e_0]$$\end{document}, for which periodic solutions of r¨=-Ueff′(r,ℓ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{r}=-U'_{\mathrm{eff}}(r, \ell )$$\end{document} do exist; see Appendix I, Section A.1, for more information.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Birman-Schwinger Principle in Galactic DynamicsOn the Period Function T1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_1$$\end{document}

Part of the Progress in Mathematical Physics Book Series (volume 77)
23 pages

/lp/springer-journals/a-birman-schwinger-principle-in-galactic-dynamics-on-the-period-FMcRfQYy6m
Publisher
Springer International Publishing
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-75185-2
Pages
29 –52
DOI
10.1007/978-3-030-75186-9_3
Publisher site
See Chapter on Publisher Site

### Abstract

[Associated with every effective potential, Ueff(r,ℓ)=UQ(r)+ℓ22r2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{\mathrm{eff}}(r, \ell )=U_Q(r)+\frac{\ell ^2}{2r^2}$$\end{document} is a period function T1(·,ℓ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_1(\cdot , \ell )$$\end{document} that is defined for certain energies e∈[emin(ℓ),e0]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e\in [e_{\mathrm{min}}(\ell ), e_0]$$\end{document}, for which periodic solutions of r¨=-Ueff′(r,ℓ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{r}=-U'_{\mathrm{eff}}(r, \ell )$$\end{document} do exist; see Appendix I, Section A.1, for more information.]

Published: Aug 14, 2021