Complex Quadratic Polynomial - Forms

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

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