Fonctionne avec Indico
v3.2.9
The moduli space of all degree D rational maps is an orbifold of dimension 2D−2. We present a language for describing dynamically natural subspaces, for example, the loci of maps having • specified critical orbit relations, • cycles of specified period and multiplier, • parabolic cycles of specified degeneracy and index, • Herman ring cycles of specified rotation number, or some combination thereof. We present a methodology for proving the smoothness and transversality of such loci. The natural setting for the discussion is a family of deformation spaces arising functorially from first principles in Teichmuller theory. Transversality ¨ flows from an infinitesimal rigidity principle (following Thurston), in the corresponding variational theory viewed cohomologically (following Kodaira-Spencer). Results for deformation spaces may then be transferred to moduli space. Moreover, the deformation space formalism and associated transversality principles apply more generally to finite type transcendental maps.