Displaying similar documents to “Non-uniformly hyperbolic billiards”

Ergodic theory for the one-dimensional Jacobi operator

Carmen Núñez, Rafael Obaya (1996)

Studia Mathematica

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We determine the number and properties of the invariant measures under the projective flow defined by a family of one-dimensional Jacobi operators. We calculate the derivative of the Floquet coefficient on the absolutely continuous spectrum and deduce the existence of the non-tangential limit of Weyl m-functions in the L 1 -topology.

Dynamics of quadratic polynomials : complex bounds for real maps

Mikhail Lyubich, Michael Yampolsky (1997)

Annales de l'institut Fourier

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We prove complex bounds for infinitely renormalizable real quadratic maps with essentially bounded combinatorics. This is the last missing ingredient in the problem of complex bounds for all infinitely renormalizable real quadratics. One of the corollaries is that the Julia set of any real quadratic map z ↦ z 2 + c , c ∈ [ - 2 , 1 / 4 ] , is locally connected.