Complex Quadratic Polynomial

Article Index for
Complex

Shopping
Quadratic

Website Links For
Complex

Information About

Complex Quadratic Polynomial

When it creates Discrete Dynamical System :

:

z_{n+1} = P_c(z_n) \,

it is named Quadratic Map .

SPECIAL CASE

The Monic , Centered complex quadratic polynomial in one Variable

z\,

and one Parameter

c\,

:

P_c(z) = z^2 +c\,

is

the simplest form of a Nonlinear Function with one Coefficient ,

a univariate Polynomial ( it has one Variable ),

a unicritical polynomial, i.e. it has one Critical Point ,

a Unimodal Function ,

a Rational Function ,

an Entire Function .

A Critical Point of complex quadratic polynomial is a point ''z'' such that

:

P_c'(z) = 0. \,

Since

:

P_c'(z) = rac{d\bigl(P_c(z)\bigr)}{dz} = 2z =0

implies

:

z = 0\,

we see that the only critical point of

P_c(z)

is the point

z = 0\,

.

REFERENCES

M. Nevins and D. Rogers, "Quadratic maps as dynamical systems on the p-adic numbers"

SEE ALSO

Misiurewicz Point

Periodic Points Of Complex Quadratic Mappings