Related papers: Statistical properties of one-dimensional maps und…

There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, "hyperbolic". We show that for a sufficiently regular one-dimensional map satisfying a weak hyperbolicity assumption,…

We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations…

Non-statistical weak measurements yield weak values that are outside the range of eigenvalues and are not rare, suggesting that weak values are a property of every pre-and-post-selected ensemble. They also extend the applicability and valid…

A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…

Recently, weak measurements have attracted a lot of interest as an experimental method for the investigation of non-classical correlations between observables that cannot be measured jointly. Here, I explain how the complex valued…

A precise definition of "weak [quantum] measurements" and "weak value" (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function…

Precise definitions of "weak [quantum] measurements" and "weak value" [of a quantum observable] are offered, which seem to capture the meaning of the often vague ways that these terms are used in the literature. Simple finite dimensional…

We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…

The emergence of realistic properties is a key problem in understanding the quantum-to-classical transition. In this respect, measurements represent a way to interface quantum systems with the macroscopic world: these can be driven in the…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

For strongly dissipative H\'enon maps at the first bifurcation where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set, we establish a thermodynamic formalism, i.e., prove the existence and…

We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…

We consider diffeomorphisms of a compact manifold with a dominated splitting which is hyperbolic except for a "small" subset of points (Hausdorff dimension smaller than one, e.g. a denumerable subset) and prove the existence of physical…

We construct SRB measures for endomorphisms satisfying conditions far weaker than the non-uniformly expansion. As a consequence, the definition of non-uniformly expanding map can be weakened. We also prove the existence of an absolutely…

We prove that any graph of multicurves satisfying certain natural properties is either hyperbolic, relatively hyperbolic, or thick. Further, this geometric characterization is determined by the set of subsurfaces that intersect every vertex…

Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only…

We introduce numerical algebraic geometry methods for computing lower bounds on the reach, local feature size, and the weak feature size of the real part of an equidimensional and smooth algebraic variety using the variety's defining…

We extend the idea of weak measurements to the general case, provide a complete treatment and obtain results for both the regime when the pre-selected and post-selected states (PPS) are almost orthogonal and the regime when they are exactly…