Transverse foliations in the rotating Kepler problem-Reference-Cited by-同舟云学术

Transverse foliations in the rotating Kepler problem

Published:2024-01-19 Issue:1 Volume:26 Page:
ISSN:1661-7738
Container-title:Journal of Fixed Point Theory and Applications
language:en
Short-container-title:J. Fixed Point Theory Appl.

Author:

Kim Seongchan

Abstract

AbstractWe construct finite energy foliations and transverse foliations of neighbourhoods of the circular orbits in the rotating Kepler problem for all negative energies. This paper would be a first step towards our ultimate goal that is to recover and refine McGehee’s results on homoclinics [23] and to establish a theoretical foundation to the numerical demonstration of the existence of a homoclinic–heteroclinic chain in the planar circular restricted three-body problem [20], using pseudoholomorphic curves.

Funder

National Research Foundation of Korea

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s11784-023-01090-8.pdf

Reference28 articles.

1. Abraham, R., Marsden, J.E.: Foundations of mechanics. Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., (1978). Second edition, revised and enlarged, With the assistance of Tudor Raţiu and Richard Cushman

2. Albers, P., Fish, J.W., Frauenfelder, U., van Koert, O.: The Conley–Zehnder indices of the rotating Kepler problem. Math. Proc. Camb. Philos. Soc. 154(2), 243–260 (2013)

3. Albers, P., Frauenfelder, U., van Koert, O., Paternain, G.P.: Contact geometry of the restricted three-body problem. Comm. Pure Appl. Math. 65(2), 229–263 (2012)

4. de Oliveira, C.L.: 3–2–1 foliations for Reeb flows on the tight 3–sphere. arXiv preprint, (2021)

5. de Paulo, N.V., Hryniewicz, U.L., Kim, S., Salomão, P.A.S.: Genus zero transverse foliations for weakly convex Reeb flows on the tight $$3$$-sphere. preprint, (2022)