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quadratic complex - translation to ρωσικά

QUADRATIC POLYNOMIAL

Quadratic map; Complex quadratic map

$* f_c planes (all other planes for c \ne 0)$
$: z_n' = \frac{d}{dc} f_c^n(z_0).$
$: z_0' = \frac{d}{dc} f_c^0(z_0) = 1$
$: z_{n+1}' = \frac{d}{dc} f_c^{n+1}(z_0) = 2\cdot{}f_c^n(z)\cdot\frac{d}{dc} f_c^n(z_0) + 1 = 2 \cdot z_n \cdot z_n' +1.$
$: f_c'(z_0) = \frac{d}{dz}f_c(z_0) = 2z_0 .$
$: (f_c^p)'(z_0) = \frac{d}{dz}f_c^p(z_0) = \prod_{i=0}^{p-1} f_c'(z_i) = 2^p \prod_{i=0}^{p-1} z_i = \lambda$
$:z'_n= 2*z_{n-1}*z'_{n-1}.$
$: (Sf)(z) = \frac{f'''(z)}{f'(z)} - \frac{3}{2} \left ( \frac{f''(z)}{f'(z)}\right ) ^2 .$
$*[https://web.archive.org/web/20040828174339/http://www.math.sunysb.edu/cgi-bin/thesis.pl?thesis02-3 Wolf Jung : Homeomorphisms on Edges of the Mandelbrot Set. Ph.D. thesis of 2002]$

Parameter plane types> MandelbrotLambda.jpg|r parameter plane ( logistic map) MandelbrotMuDouadyRabbit.jpg| c parameter plane </gallery> The [[phase space]] of a quadratic map is called its '''parameter plane'''. Here: <math>z_0 = z_{cr}</math> is constant and <math>c</math> is variable. There is no dynamics here. It is only a set of parameter values. There are no orbits on the parameter plane. The parameter plane consists of: * The [[Mandelbrot set]] ** The [[bifurcation locus]] = boundary of [[Mandelbrot set]] with *** root points ** Bounded hyperbolic components of the Mandelbrot set = interior of Mandelbrot set<ref>[http://arxiv.org/abs/0805.1658 [[Lasse Rempe]], Dierk Schleicher : Bifurcation Loci of Exponential Maps and Quadratic Polynomials: Local Connectivity, Triviality of Fibers, and Density of Hyperbolicity]{{Dead link|date=July 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> with internal rays * exterior of Mandelbrot set with ** [[external ray]]s ** equipotential lines There are many different subtypes of the parameter plane.<ref>[http://aleph0.clarku.edu/~djoyce/julia/altplane.html Alternate Parameter Planes by David E. Joyce ]</ref><ref>[http://mrob.com/pub/muency/exponentialmap.html exponentialmap by Robert Munafo]</ref> [[File:Mandelbrot set - multiplier map.png|thumb|right|Multiplier map]] See also : * [[External ray#Uniformization 2|Boettcher map]] which maps exterior of Mandelbrot set to the exterior of unit disc * multiplier map which maps interior of hyperbolic component of Mandelbrot set to the interior of unit disc ====2D Dynamical plane==== <blockquote>

quadratic complex

математика

квадратичный комплекс

quadratic field

ALGEBRAIC NUMBER FIELD OF DEGREE TWO OVER THE RATIONAL NUMBERS

Imaginary quadratic field; Imaginary quadratic number field; Quadratic fields; Real quadratic field; Complex quadratic field; Quadratic number field

математика

квадратичное поле

quadratic irrationality

MATHEMATICAL CONCEPT

Quadratic surd; Quadratic irrationality; Quadratic Irrational Number; Quadratic irrationalities; Quadratic irrational; Quadratic irrational numbers

математика

квадратичная иррациональность

Ορισμός

quadratic

[kw?'drat?k]

¦ adjective Mathematics involving the second and no higher power of an unknown quantity or variable.

Origin

C17: from Fr. quadratique or mod. L. quadraticus, from quadratus, quadrare (see quadrate).

Εμφάνιση περισσότερων ορισμών

Βικιπαίδεια

Complex quadratic polynomial

A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers.

https://en.wikipedia.org/wiki/Complex quadratic polynomial

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