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We prove that for every polynomial of one complex variable of degree at least2 and Julia set not being totally disconnected nor a circle, nor interval,Hausdorff dimension of this Julia set is larger than 1. Till now this was knownonly in the connected Julia set case. We give also an example of a polynomialwith non-connected but not totally disconnected Julia set and such that all itscomponents comprising of more than single points are analytic arcs, thusresolving a question by Christopher Bishop, who asked whether every suchcomponent must have Hausdorff dimension larger than 1.

On Hausdorff dimension of polynomial not totally disconnected Julia sets