In mathematics, a Lattès map is a
rational map
In mathematics, in particular the subfield of algebraic geometry, a rational map or rational mapping is a kind of partial function between algebraic varieties. This article uses the convention that varieties are irreducible.
Definition
Formal d ...
''f'' = Θ''L''Θ
−1 from the
complex sphere
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane: the complex plane plus one point at infinity. This extended plane represents the extended complex numbers, that is, the complex numbers ...
to itself such that Θ is a
holomorphic map
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex derivat ...
from a
complex torus
In mathematics, a complex torus is a particular kind of complex manifold ''M'' whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian product of some number ''N'' circles). Here ''N'' must be the even number 2''n'', whe ...
to the complex sphere and ''L'' is an affine map ''z'' → ''az'' + ''b'' from the complex torus to itself.
Lattès maps are named after French mathematician
Samuel Lattès, who wrote about them in 1918.
References
*
*
{{DEFAULTSORT:Lattes map
Dynamical systems