A dynamical invariant for Sierpiński cardioid Julia sets

• Autorzy: Paul Blanchard , Daniel Cuzzocreo , Robert L. Devaney , Elizabeth Fitzgibbon , Stefano Silvestri
• Języki publikacji: EN

Abstrakty

EN

For the family of rational maps zⁿ + λ/zⁿ where n ≥ 3, it is known that there are infinitely many small copies of the Mandelbrot set that are buried in the parameter plane, i.e., they do not extend to the outer boundary of this set. For parameters lying in the main cardioids of these Mandelbrot sets, the corresponding Julia sets are always Sierpiński curves, and so they are all homeomorphic to one another. However, it is known that only those cardioids that are symmetrically located in the parameter plane have conjugate dynamics. We produce a dynamical invariant that explains why these maps have different dynamics.

Kategorie tematyczne

• 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 226
• Numer: 3
• Strony: 253-277

Daty

wydano

2014

Twórcy

autor

Paul Blanchard

• Department of Mathematics, Boston University, 111 Cummington Mall, Boston, MA 02215, U.S.A.

autor

Daniel Cuzzocreo

• Department of Mathematics, Boston University, 111 Cummington Mall, Boston, MA 02215, U.S.A.

autor

Robert L. Devaney

• Department of Mathematics, Boston University, 111 Cummington Mall, Boston, MA 02215, U.S.A.

autor

Elizabeth Fitzgibbon

• Department of Mathematics, Boston University, 111 Cummington Mall, Boston, MA 02215, U.S.A.

autor

Stefano Silvestri

• Department of Mathematics, Boston University, 111 Cummington Mall, Boston, MA 02215, U.S.A.

Identyfikatory

DOI

10.4064/fm226-3-5