An Attracting Dynamics is a triple (f,W,a), where W is an open subset of the R(iemann) S(phere), f is a holomorphic map from W into the RS and a is an attracting periodic point for f. Denote by B(a) the attracted basin of the orbit of a for f. Two attracting dynamics (f,W,a) and (f',W',a') are i) conformally equivalent iif there is a Möbius transformation M which maps a to a' and which conjugates dynamics. or ii) hybridly equivalent iff there exists a quasi conformal homeomorphism of RS to itself which maps a to a', which conjugates dynamics and with dbar derivative identically zero on the complement of B(a). The moduli space for the attracting dynamics (f,W,a) is the space of attractings dynamics (f,W,a') which are hybridly equivalent to (f,W,a). The talk will discuss properties of moduli spaces of different attracting dynamics.
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24th Nordic and 1st Franco-Nordic Congress of Mathematicians, 2005