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, such as in a parametric curve. Examples include the mathematical models ...

s, the Cantor tree is an infinite-

genus Genus (; : genera ) is a taxonomic rank above species and below family (taxonomy), family as used in the biological classification of extant taxon, living and fossil organisms as well as Virus classification#ICTV classification, viruses. In bino ...

surface

homeomorphic In mathematics and more specifically in topology, a homeomorphism ( from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function betw ...

to a

sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, 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 mentioned by German mathematician Georg Cantor in 1883. Throu ...

removed. The blooming Cantor tree is a Cantor tree with an infinite number of handles added in such a way that every

end End, END, Ending, or ENDS may refer to: End Mathematics *End (category theory) * End (topology) * End (graph theory) * End (group theory) (a subcase of the previous) * End (endomorphism) Sports and games *End (gridiron football) *End, a division ...

is a limit of handles.

References

{{reflist, refs= {{Citation , last1=Ghys , first1=Étienne , title=Topologie des feuilles génériques , doi=10.2307/2118526 , mr=1324140 , year=1995 , journal=

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

, series=Second Series , issn=0003-486X , volume=141 , issue=2 , pages=387–422, jstor=2118526 , language=fr {{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, pag
210
} Fractals Surfaces Eponyms in geometry

See also

References