Fitting Invariant Curves on Billiard Tables and the Birkhoff-Herman Theorem

Edoh Y. Amiran ()
Additional contact information
Edoh Y. Amiran: Western Washington University

A chapter in New Advances in Celestial Mechanics and Hamiltonian Systems, 2004, pp 29-36 from Springer

Abstract: A two-dimensional billiard table is geometrically integrable when the phase space is foliated by continuous invariant curves. When an integrable planar domain has a C 4 boundary with strictly positive curvature, a neighborhood of the boundary is foliated by invariant circles. This family of invariant circles can lose convexity only after developing a singularity and if it developes a singularity, the boundary contains a segment of an ellipse. An important role in this result is played by the Birkhoff-Herman thoerem which shows that differentiability of enveloped curves cannot be lost without a change in homotopy type.

Keywords: billiard map; integrable; invariant curves; Birkhoff-Herman theorem (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-9058-7_2

Ordering information: This item can be ordered from
http://www.springer.com/9781441990587

DOI: 10.1007/978-1-4419-9058-7_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().