Computer generated images of dynamical sets (such
as Julia sets) play a
prominent role in establishing new results. Roughly speaking, computational
complexity of such set measures how hard it is to draw an approximation of
the set with a given accuracy using a computer. It is known that already the
class of quadratic polynomials contains examples with non-computable Julia
sets (for them there is no algorithm which could draw an approximation
with arbitrary precision) and examples with Julia sets of arbitrarily high
computational complexity.
In this talk I will show that for a large class of rational maps
(satisfying
Exponential Shrinking Condition) including almost all real polynomials
$p_c (z) = z^2+c$; $c \in \mathbb R$, the Julia set has polynomial time complexity.
The talk
is based on a joint work with Michael Yampolsky.