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:
“Ye know why the forms are fair, ye hear how the tale is told:
It is all triumphant art, but art in obedience to laws,”
—Robert Browning (1812–1889)
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—Barbara Howar (b. 1934)
“It is given to few to add the store of knowledge, to strike new springs of thought, or to shape new forms of beauty. But so sure as it is that men live not by bread, but by ideas, so sure is it that the future of the world lies in the hands of those who are able to carry the interpretation of nature a step further than their predecessors.”
—Thomas Henry Huxley (1825–95)