Forms
When the quadratic polynomial has only one variable ( univariate ), one can distinguish its 4 main forms:
- The general form : where .
- The factored form used for logistic map
- which has an indifferent fixed point with multiplier at the origin
- The monic and centered form,
The monic and centered form has the following properties:
- It is the simplest form of a nonlinear function with one coefficient (parameter),
- It is an unicritical polynomial, i.e. it has one critical point,
- It is a centered polynomial (the sum of its critical points is zero),
- It can be postcritically finite, i.e. If the orbit of the critical point is finite. It is when critical point is periodic or preperiodic.
- It is a unimodal function,
- It is a rational function,
- It is an entire function.
Read more about this topic: Complex Quadratic Polynomial
Famous quotes containing the word forms:
“I may not tell
of the forms that pass and pass,
of that constant old, old face
that leaps from each wave
to wait underneath the boat
in the hope that at last she’s lost.”
—Hilda Doolittle (1886–1961)
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—Angela Davis (b. 1944)
“I am not so foolish as to declaim against forms. Forms are as essential as bodies; but to exalt particular forms, to adhere to one form a moment after it is outgrown, is unreasonable, and it is alien to the spirit of Christ.”
—Ralph Waldo Emerson (1803–1882)