S-unimodal Misiurewicz maps with flat critical points

• Autorzy: Roland Zweimüller
• Języki publikacji: EN

Abstrakty

EN

We consider S-unimodal Misiurewicz maps T with a flat critical point c and show that they exhibit ergodic properties analogous to those of interval maps with indifferent fixed (or periodic) points. Specifically, there is a conservative ergodic absolutely continuous σ-finite invariant measure μ, exact up to finite rotations, and in the infinite measure case the system is pointwise dual ergodic with many uniform and Darling-Kac sets. Determining the order of return distributions to suitable reference sets we obtain bounds on the decay of correlations and on wandering rates. Assuming some control of the local behaviour of T at c, we show that in most cases, e.g. whenever the postcritical orbit has a Lyapunov exponent, the tail of the return distribution is in fact regularly varying, which implies various distributional limit theorems.

Kategorie tematyczne

• 37A25: Ergodicity, mixing, rates of mixing
• 37A40: Nonsingular (and infinite-measure preserving) transformations
• 60F05: Central limit and other weak theorems
• 28D05: Measure-preserving transformations
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 181
• Numer: 1
• Strony: 1-25

Daty

wydano

2004

Twórcy

autor

Roland Zweimüller

• Mathematics Department, Imperial College London, 180 Queen's Gate, London SW7 2AL, UK

Identyfikatory

DOI

10.4064/fm181-1-1