다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Recurrence plots for the analysis of complex systems

/pdf/introduction-to-the-modern-theory-of-dynamical-systems-1eced70mum.pdf

Introduction to the Modern Theory of Dynamical Systems

The setting of this paper consists of a map making “nice” returns to a reference set. Criteria for the existence of equilibria, speed of convergence to equilibria and for the central limit theorem are given in terms of the tail of the return time function. The abstract setting considered arises naturally in differentiable dynamical systems with some expanding or hyperbolic properties.

Recurrence times and rates of mixing

We present an original approach which allows us to investigate the statistical properties of a non-uniformly hyperbolic map on the interval. Based on a stochastic approximation of the deterministic map, this method essentially gives the optimal polynomial bound for the decay of correlations, the degree depending on the order of the tangency at the neutral fixed point.

A probabilistic approach to intermittency

In this paper we provide general estimates for the errors between the distribution of the first, and more generally, the K

 th return time (suitably rescaled) and the Poisson law for measurable dynamical systems. In the case that the system exhibits strong mixing properties, these bounds are explicitly expressed in terms of the speed of mixing. Using these approximations, the Poisson law is finally proved to hold for a large class of non hyperbolic systems on the interval.

/pdf/statistics-of-return-times-a-general-framework-and-new-1c9p8k93u9.pdf

Statistics of Return Times:¶A General Framework and New Applications

We investigate the existence and statistical properties of absolutely continuous invariant measures for multidimensional expanding maps with singularities. The key point is the establishment of a spectral gap in the spectrum of the transfer operator. Our assumptions appear quite naturally for maps with singularities. We allow maps that are discontinuous on some extremely wild sets, the shape of the discontinuities being completely ignored with our approach.

/pdf/absolutely-continuous-invariant-measures-for-55s2j6s2dc.pdf

Absolutely continuous invariant measures for multidimensional expanding maps

We study the quantitative behavior of Poincar e recurrence. In particular, for an equilibrium measure on a locally maximal hyper- bolic set of a C 1+ dieomorphism f, we show that the recurrence rate to each point coincides almost everywhere with the Hausdor dimen- sion d of the measure, that is, inffk > 0 : f k x2 B(x;r)g r d . This result is a non-trivial generalization of work of Boshernitzan concerning the quantitative behavior of recurrence, and is a dimensional version of work of Ornstein and Weiss for the entropy. We stress that our ap- proach uses dierent techniques. Furthermore, our results motivate the introduction of a new method to compute the Hausdor dimension of measures.

/pdf/hausdorff-dimension-of-measures-via-poincar-e-recurrence-2651nh6a8l.pdf

Hausdorff dimension of measures via poincar e recurrence

We establish a \" conditional \" variational principle, which unifies and extends many results in the multifractal analysis of dynam-ical systems. Namely, instead of considering several quantities of local nature and studying separately their multifractal spectra we develop a unified approach which allows us to obtain all spectra from a new mul-tifractal spectrum. Using the variational principle we are able to study the regularity of the spectra and the full dimensionality of their irregular sets for several classes of dynamical systems, including the class of maps with upper semi-continuous metric entropy. Another application of the variational principle is the following. The multifractal analysis of dynamical systems studies multifractal spectra such as the dimension spectrum for pointwise dimensions and the en-tropy spectrum for local entropies. It has been a standing open problem to effect a similar study for the \" mixed \" multifractal spectra, such as the dimension spectrum for local entropies and the entropy spectrum for pointwise dimensions. We show that they are analytic for several classes of hyperbolic maps. We also show that these spectra are not necessarily convex, in strong contrast with the \" non-mixed \" multifractal spectra.

/pdf/variational-principles-and-mixed-multifractal-spectra-44sk6eroeu.pdf

Benoît Saussol

Papers

A probabilistic approach to intermittency

Statistics of Return Times:¶A General Framework and New Applications

Absolutely continuous invariant measures for multidimensional expanding maps

Hausdorff dimension of measures via poincar e recurrence

Variational principles and mixed multifractal spectra