Roeder, RolandKaschner, Scott R.Bleher, Pavel, 1947-Misiurewicz, Michał, 1948-Buzzard, GregoryMukhin, Evgeny2013-12-102013-12-102013-12-10https://hdl.handle.net/1805/3749http://dx.doi.org/10.7912/C2/2396Indiana University-Purdue University Indianapolis (IUPUI)Let f:X\rightarrow X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n > 1. Suppose there is an embedded copy of \mathbb P^1 that is invariant under f, with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose also that f restricted to this line is given by z\rightarrow z^b, with resulting invariant circle S. We prove that if a ≥ b, then the local stable manifold W^s_loc(S) is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider contexts. We then show that the condition a ≥ b cannot be relaxed without adding additional hypotheses by resenting two examples with a < b for which W^s_loc(S) is not real analytic in the neighborhood of any point.en-USMathematical analysis -- ResearchManifolds (Mathematics)Differential equations, Nonlinear -- Numerical solutionsInvariant manifolds -- AnalysisDifferentiable dynamical systemsDifferential topologyFunctions of complex variablesMappings (Mathematics) -- AnalysisAlgebraic cycles