Related papers: Quantitative Recurrence for Generic Homeomorphisms

We survey the distributional properties of progressively dilating sets under projection by covering maps, focusing on manifolds of constant sectional curvature. In the Euclidean case, we review previously known results and formulate some…

While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…

It is proved that whenever two aperiodic repetitive tilings with finite local complexity have homeomorphic tiling spaces, their associated complexity functions are asymptotically equivalent in a certain sense (which implies, if the…

We review the status of a program, outlined and motivated in the introduction, for the study of correspondences between spectral invariants of partially hyperbolic flows on locally symmetric spaces and their quantizations. Further we…

We prove that a topological homeomorphism conjugating two generic 1-parameter unfoldings of 1-variable complex analytic resonant diffeomorphisms is holomorphic or anti-holomorphic by restriction to the unperturbed parameter. We provide…

A standard problem in applied topology is how to discover topological invariants of data from a noisy point cloud that approximates it. We consider the case where a sample is drawn from a properly embedded C1-submanifold without boundary in…

We describe of the topology of the geometric quotients of 2n dimensional compact connected symplectic manifolds with n-1 dimensional torus actions. When the isotropy weights at each fixed point are in general position, the quotient is…

The generic singularities and bifurcations are classified for one-parameter families of curves with frames in a space form, the Euclidean space, the elliptic space or the hyperbolic space via projective geometry. Two kinds of frames are…

When identified with sequences of irreducible Hermitian-Einstein connections, sequences of stable holomorphic bundles of fixed topological type and bounded degree on a compact complex surface equipped with a Gauduchon metric are shown to…

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…

By means of hypercyclic operator theory, we complement our previous results on hypercyclic holomorphic maps between complex Euclidean spaces having slow growth rates,by showing {\it abstract abundance} rather than {\it explicit existence}.…

Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…

We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…

Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…

Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…

We deal with topological spaces homeomorphic to their respective squares. Primarily, we investigate the existence of large families of such spaces in some subclasses of compact metrizable spaces. As our main result we show that there is a…

Polynomial ensembles are determinantal point processes associated with (non necessarily orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put forward the use of recurrence coefficients to obtain the…

We give a unified treatment of decay of correlations for nonuniformly expanding systems with a good inducing scheme. In addition to being more elementary than previous treatments, our results hold for general integrable return time…

We have proved that homeomorphisms of domains of Euclidean space, inverse of which distort the modulus of families of curves by Poletskii type, have a continuous extension to isolated boundary point.

In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…