A cell decomposition for marked cycle curves
Abstract
We describe a family Cycp(F) of marked cycle curves that parameterize the cycles of period p of a given family F of dynamical systems. We produce algorithms to compute a canonical cell decomposition for the marked cycle curves over the family Per1(0) of quadratic polynomials as well as over the family Per2(0) of quadratic rational maps with a critical 2-cycle. We obtain formulas for the number of d-cells in these decompositions, giving rise to e.g. a formula for their genus.
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