In
dynamical system
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...
s, the Cantor tree is an infinite-
genus
Genus ( plural genera ) is a taxonomic rank used in the biological classification of extant taxon, living and fossil organisms as well as Virus classification#ICTV classification, viruses. In the hierarchy of biological classification, genus com ...
surface
homeomorphic
In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphi ...
to a
sphere
A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
with a
Cantor set
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.
Thr ...
removed. The blooming Cantor tree is a Cantor tree with an infinite number of handles added in such a way that every end is a limit of handles.
See also
*
Jacob's ladder surface
In mathematics, Jacob's ladder is a surface with infinite genus and two ends. It was named after Jacob's ladder by Étienne , because the surface can be constructed as the boundary of a ladder that is infinitely long in both directions.
See al ...
*
Loch Ness monster surface
In mathematics, the Loch Ness monster is a surface with infinite genus but only one end. It appeared named this way already in a 1981 article by . The surface can be constructed by starting with a plane (which can be thought of as the surface ...
References
*
*{{Citation , last1=Walczak , first1=Paweł , title=Dynamics of foliations, groups and pseudogroups , url=https://books.google.com/books?id=Tl4WkcHzhIAC , publisher=Birkhäuser Verlag , series=Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series)
athematics Institute of the Polish Academy of Sciences. Mathematical Monographs (New Series), isbn=978-3-7643-7091-6 , mr=2056374 , year=2004 , volume=64
Surfaces