= Critical orbit of a rational map
{title2=$p,R(p),R^2(p),\ldots$}
= Critical orbit
{synonym}
= Critical orbits of a rational map
{synonym}
A critical orbit is the forward sequence $p,R(p),R^2(p),\ldots$ starting at a <critical point of a rational map>. The <postcritical set> records the forward images, usually from the first iterate onward, of all critical points; a single critical orbit and the union of all such images are distinct notions. For quadratic polynomials there is one finite critical point, zero, and its orbit controls connectedness of the filled Julia set and membership in the <Mandelbrot set>. A bounded orbit can be preperiodic to a repelling cycle, as $0\mapsto i\mapsto-1+i\mapsto-i\mapsto-1+i$ for $z^2+i$; boundedness then does not imply Fatou membership.
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