Outer billiards
Type of dynamical system in mathematics
Outer billiards is a dynamical system based on a convex shape in the plane. Classically, this system is defined for the Euclidean plane, but one can also consider the system in the hyperbolic plane or in other spaces that suitably generalize the plane. Outer billiards differs from a usual dynamical billiard in that it deals with a discrete sequence of moves outside the shape rather than inside of it.
Definitions
The outer billiards map
Let P be a convex shape in the plane. Given a point x0 outside P, there is typically a unique point x1 (also outside P) so that the line segment connecting x0 to x1 is tangent to P at its midpoint, and a person walking from x0 to x1 would see P on the right (see the figure). The map F: x0 → x1 is called the outer billiards map.
The inverse (or backwards) outer billiards map is also defined, as the map x1 → x0. One gets the inverse map simply by replacing the word right by the word left in the definition given above.
The figure shows the situation in the Euclidean plane, but the definition in the hyperbolic plane is essentially the same.
Orbits
An outer billiards orbit is the set of all iterations of the point, namely ...
The public source identifies “Outer billiards” as type of dynamical system in mathematics. This brief keeps that definition visible, then builds a research path around Outer, billiards and Type.
Why this record matters
A short description can identify a subject without explaining its stakes. For “Outer billiards”, the useful work is to connect “type of dynamical system in mathematics” to the records capable of establishing context and consequence.
Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Sep 22, 2026. The linked authority identifier is Q7112021. None of the 0 selected statements returned an explicit reference.
Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Outer billiards”, its source revision and the description used here.
- Expand the search: follow Outer billiards primary sources, Outer billiards archive and Outer research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Outer billiards”?
- What terminology or title could unlock a more precise catalogue search?
- Which institution is responsible for the underlying evidence?
Search terms from this dossier
This entry incorporates text from “Outer billiards” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.