Deformation of Geometry and Bifurcations of Vortex Rings

James Montaldi; Tadashi Tokieda

doi:10.1007/978-3-0348-0451-6_14

Deformation of Geometry and Bifurcations of Vortex Rings

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool. © Springer Basel 2013.

Original language	English
Title of host publication	Springer Proceedings in Mathematics and Statistics\|Springer Proc. Math. Stat.
Subtitle of host publication	Proceedings of a Conference in Honor of Jürgen Scheurle
Place of Publication	Basel
Publisher	Springer Nature
Pages	335-370
Number of pages	35
Volume	35
DOIs	https://doi.org/10.1007/978-3-0348-0451-6_14
Publication status	Published - 2013
Event	2012 International Conference Recent Trends in Dynamical Systems - Munich Duration: 1 Jul 2013 → … http://www.springer.com/series/10533

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Publisher	Springer New York LLC
Volume	35

Other

Other	2012 International Conference Recent Trends in Dynamical Systems
City	Munich
Period	1/07/13 → …
Internet address	http://www.springer.com/series/10533

Access to Document

10.1007/978-3-0348-0451-6_14

Cite this

Montaldi, J., & Tokieda, T. (2013). Deformation of Geometry and Bifurcations of Vortex Rings. In Springer Proceedings in Mathematics and Statistics|Springer Proc. Math. Stat.: Proceedings of a Conference in Honor of Jürgen Scheurle (Vol. 35, pp. 335-370). (Springer Proceedings in Mathematics & Statistics; Vol. 35). Springer Nature. https://doi.org/10.1007/978-3-0348-0451-6_14

@inbook{cab845dd9005446b8c397241c5bdfab5,

title = "Deformation of Geometry and Bifurcations of Vortex Rings",

abstract = "We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool. {\textcopyright} Springer Basel 2013.",

author = "James Montaldi and Tadashi Tokieda",

year = "2013",

doi = "10.1007/978-3-0348-0451-6_14",

language = "English",

volume = "35",

series = "Springer Proceedings in Mathematics & Statistics",

publisher = "Springer Nature",

pages = "335--370",

booktitle = "Springer Proceedings in Mathematics and Statistics|Springer Proc. Math. Stat.",

address = "United States",

note = "2012 International Conference Recent Trends in Dynamical Systems ; Conference date: 01-07-2013",

url = "http://www.springer.com/series/10533",

}

Montaldi, J & Tokieda, T 2013, Deformation of Geometry and Bifurcations of Vortex Rings. in Springer Proceedings in Mathematics and Statistics|Springer Proc. Math. Stat.: Proceedings of a Conference in Honor of Jürgen Scheurle. vol. 35, Springer Proceedings in Mathematics & Statistics, vol. 35, Springer Nature, Basel, pp. 335-370, 2012 International Conference Recent Trends in Dynamical Systems, Munich, 1/07/13. https://doi.org/10.1007/978-3-0348-0451-6_14

Deformation of Geometry and Bifurcations of Vortex Rings. / Montaldi, James; Tokieda, Tadashi.
Springer Proceedings in Mathematics and Statistics|Springer Proc. Math. Stat.: Proceedings of a Conference in Honor of Jürgen Scheurle. Vol. 35 Basel: Springer Nature, 2013. p. 335-370 (Springer Proceedings in Mathematics & Statistics; Vol. 35).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Deformation of Geometry and Bifurcations of Vortex Rings

AU - Montaldi, James

AU - Tokieda, Tadashi

PY - 2013

Y1 - 2013

N2 - We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool. © Springer Basel 2013.

AB - We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool. © Springer Basel 2013.

U2 - 10.1007/978-3-0348-0451-6_14

DO - 10.1007/978-3-0348-0451-6_14

M3 - Chapter

VL - 35

T3 - Springer Proceedings in Mathematics & Statistics

SP - 335

EP - 370

BT - Springer Proceedings in Mathematics and Statistics|Springer Proc. Math. Stat.

PB - Springer Nature

CY - Basel

T2 - 2012 International Conference Recent Trends in Dynamical Systems

Y2 - 1 July 2013

ER -

Deformation of Geometry and Bifurcations of Vortex Rings

Abstract

Publication series

Other

Access to Document

Fingerprint

Cite this