# American Institute of Mathematical Sciences

October  2011, 29(4): 1405-1417. doi: 10.3934/dcds.2011.29.1405

## Hausdorffization and polynomial twists

 1 Department of Mathematics, Computer Science, and Statistics, University of Illinois at Chicago, Chicago, IL, United States 2 Department of Mathematics, Indiana University, Bloomington, IN, United States

Received  December 2009 Revised  October 2010 Published  December 2010

We study dynamical equivalence relations on the moduli space $\MP_d$ of complex polynomial dynamical systems. Our main result is that the critical-heights quotient $\MP_d \to \cT_d$* of [4] is the Hausdorffization of a relation based on the twisting deformation of the basin of infinity. We also study relations of topological conjugacy and the Branner-Hubbard wringing deformation.
Citation: Laura DeMarco, Kevin Pilgrim. Hausdorffization and polynomial twists. Discrete & Continuous Dynamical Systems - A, 2011, 29 (4) : 1405-1417. doi: 10.3934/dcds.2011.29.1405
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