Masato Tsujii

Positive Lyapunov exponents in families of one dimensional dynamical systems

SummaryWe give a generalization of Jakobsons theorem [Ja] and a precise estimate for the density of parameters corresponding to systems with absolutely continuous invariant measures.

Quasi-compactness of transfer operators for contact Anosov flows

For any Cr contact Anosov flow with r ≥ 3, we construct a scale of Hilbert spaces, which are embedded in the space of distributions on the phase space and contain all the Cr functions, such that the one-parameter family of transfer operators for the flow extend to them boundedly and that the extensions are quasi-compact. We also give explicit bounds on the essential spectral radii of those extensions in terms of differentiability r and the hyperbolicity exponents of the flow.

Weakly expanding skew-products of quadratic maps

We consider quadratic skew-products over angle-doubling of the circle and prove that they admit positive Lyapunov exponents almost everywhere and an absolutely continuous invariant probability measure. This extends corresponding results of M. Viana and J. F. Alves for skew-products over the linear strongly expanding map of the circle.

Decay of correlations in suspension semi-flows of angle-multiplying maps

We consider suspension semi-flows of angle-multiplying maps on the circle. Under a

On continuity of Bowen-Ruelle-Sinai measures in families of one dimensional maps

C^r

Zeta functions and dynamical systems

generic condition on the ceiling function, we show that there exists an anisotropic Sobolev space¥cite{BT} contained in the

Regular points for ergodic sinai measures

L^2

The partial captivity condition for U(1) extensions of expanding maps on the circle

space such that the Perron-Frobenius operator for the time-

Semiclassical Approach for the Ruelle-Pollicott Spectrum of Hyperbolic Dynamics

t

On the Fourier transforms of self-similar measures

-map act on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description on decay of correlations, which extends the result of M. Pollicott¥cite{Po}.