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Full-Text Articles in Dynamical Systems
Rational Maps Of Cp^2 With No Invariant Foliation, Scott R. Kaschner, Rodrigo A. Perez, Roland K.W. Roeder
Rational Maps Of Cp^2 With No Invariant Foliation, Scott R. Kaschner, Rodrigo A. Perez, Roland K.W. Roeder
Scholarship and Professional Work - LAS
We present simple examples of rational maps of the complex projective plane with equal first and second dynamical degrees and no invariant foliation.
Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, Scott R. Kaschner, Reaper Romero, David Simmons
Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, Scott R. Kaschner, Reaper Romero, David Simmons
Scholarship and Professional Work - LAS
We show that the geometric limit as n → ∞ of the Julia sets J(Pn,c) for the maps Pn,c(z) = zn + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.
Superstable Manifolds Of Invariant Circles And Codimension-One Böttcher Functions, Scott R. Kaschner, Roland K.W. Roeder
Superstable Manifolds Of Invariant Circles And Codimension-One Böttcher Functions, Scott R. Kaschner, Roland K.W. Roeder
Scholarship and Professional Work - LAS
Let f:X ⇢ X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n>1. Suppose that there is an embedded copy of P1 that is invariant under f, with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose that f restricted to this line is given by z↦zb, with resulting invariant circle S. We prove that if a≥b, then the local stable manifold Wsloc(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 …
Rational Map Of Cp^2 With No Invariant Foliation, Scott R. Kaschner, Rodrigo A. Perez, Roland K.W. Roeder
Rational Map Of Cp^2 With No Invariant Foliation, Scott R. Kaschner, Rodrigo A. Perez, Roland K.W. Roeder
Scholarship and Professional Work - LAS
Conference Poster presented at: Midwest Dynamical Systems Conference, Champaign/Urbana, IL November 1-3, 2013.