---
_id: '8417'
abstract:
- lang: eng
  text: The restricted planar elliptic three body problem (RPETBP) describes the motion
    of a massless particle (a comet or an asteroid) under the gravitational field
    of two massive bodies (the primaries, say the Sun and Jupiter) revolving around
    their center of mass on elliptic orbits with some positive eccentricity. The aim
    of this paper is to show the existence of orbits whose angular momentum performs
    arbitrary excursions in a large region. In particular, there exist diffusive orbits,
    that is, with a large variation of angular momentum. The leading idea of the proof
    consists in analyzing parabolic motions of the comet. By a well-known result of
    McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold
    P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable
    (resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold
    at parabolic infinity. On P∞ it is possible to define two scattering maps, which
    contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic
    both in the future and the past. Since the inner dynamics inside P∞ is trivial,
    two different scattering maps are used. The combination of these two scattering
    maps permits the design of the desired diffusive pseudo-orbits. Using shadowing
    techniques and these pseudo orbits we show the existence of true trajectories
    of the RPETBP whose angular momentum varies in any predetermined fashion.
article_processing_charge: No
article_type: original
author:
- first_name: Amadeu
  full_name: Delshams, Amadeu
  last_name: Delshams
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
- first_name: Abraham
  full_name: de la Rosa, Abraham
  last_name: de la Rosa
- first_name: Tere M.
  full_name: Seara, Tere M.
  last_name: Seara
citation:
  ama: Delshams A, Kaloshin V, de la Rosa A, Seara TM. Global instability in the restricted
    planar elliptic three body problem. <i>Communications in Mathematical Physics</i>.
    2018;366(3):1173-1228. doi:<a href="https://doi.org/10.1007/s00220-018-3248-z">10.1007/s00220-018-3248-z</a>
  apa: Delshams, A., Kaloshin, V., de la Rosa, A., &#38; Seara, T. M. (2018). Global
    instability in the restricted planar elliptic three body problem. <i>Communications
    in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s00220-018-3248-z">https://doi.org/10.1007/s00220-018-3248-z</a>
  chicago: Delshams, Amadeu, Vadim Kaloshin, Abraham de la Rosa, and Tere M. Seara.
    “Global Instability in the Restricted Planar Elliptic Three Body Problem.” <i>Communications
    in Mathematical Physics</i>. Springer Nature, 2018. <a href="https://doi.org/10.1007/s00220-018-3248-z">https://doi.org/10.1007/s00220-018-3248-z</a>.
  ieee: A. Delshams, V. Kaloshin, A. de la Rosa, and T. M. Seara, “Global instability
    in the restricted planar elliptic three body problem,” <i>Communications in Mathematical
    Physics</i>, vol. 366, no. 3. Springer Nature, pp. 1173–1228, 2018.
  ista: Delshams A, Kaloshin V, de la Rosa A, Seara TM. 2018. Global instability in
    the restricted planar elliptic three body problem. Communications in Mathematical
    Physics. 366(3), 1173–1228.
  mla: Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic
    Three Body Problem.” <i>Communications in Mathematical Physics</i>, vol. 366,
    no. 3, Springer Nature, 2018, pp. 1173–228, doi:<a href="https://doi.org/10.1007/s00220-018-3248-z">10.1007/s00220-018-3248-z</a>.
  short: A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical
    Physics 366 (2018) 1173–1228.
date_created: 2020-09-17T10:41:43Z
date_published: 2018-09-05T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '05'
doi: 10.1007/s00220-018-3248-z
extern: '1'
intvolume: '       366'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '09'
oa_version: None
page: 1173-1228
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - 0010-3616
  - 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Global instability in the restricted planar elliptic three body problem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 366
year: '2018'
...