dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...

s, the Cantor tree is an infinite-

genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial nom ...

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 isomor ...

to a

sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the c ...

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. T ...

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.

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

See also

References