On an analytic approach to the Fatou conjecture

• Autorzy: Genadi Levin
• Języki publikacji: EN

Abstrakty

EN

Let f be a quadratic map (more generally, $f(z) = z^d + c$, d > 1) of the complex plane. We give sufficient conditions for f to have no measurable invariant linefields on its Julia set. We also prove that if the series $∑_{n≥0} 1/(fⁿ)'(c)$ converges absolutely, then its sum is non-zero. In the proof we use analytic tools, such as integral and transfer (Ruelle-type) operators and approximation theorems.

Kategorie tematyczne

• 37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
• 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 171
• Numer: 2
• Strony: 177-196

Daty

wydano

2002

Twórcy

autor

Genadi Levin

• Institute of Mathematics, The Hebrew University, Givat Ram 91904, Jerusalem, Israel

Identyfikatory

DOI

10.4064/fm171-2-5