Related papers: Smooth ergodic theory
This is a reference volume on polyfold and Fredholm theory.
A brief history, the current state, and future directions of spin mechanics are presented.
The implications of the original misunderstanding of the etymology of the word "ergodic" are discussed, and the contents of a not too well known paper by Boltzmann are critically examined. The connection with the modern theory of Ruelle is…
We provide an exposition of the proofs of Bourgain's polynomial ergodic theorems. The focus is on the motivation and intuition behind his arguments.
This is an introduction to some recent developments in string theory and M theory. We try to concentrate on the main physical aspects, and often leave more technical details to the original literature.
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and…
The article is an historical overview of some of the major contributions from different areas of Science with which, for centuries, it has been built up a scientific, sound and consistent vision of the atom. Some experiments that led us to…
In this paper, we study the complicated dynamics of Anosov systems driven by an external force in the context of geometric theory (an abundance of random periodic points and random horseshoes) and smooth ergodic theory (random periodic…
This is a short expository article on alternating knots and is to appear in the Concise Encyclopedia of Knot Theory.
We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.
We describe the equivariant cohomology ring of rationally smooth projective embeddings of reductive groups. These embeddings are the projectivizations of reductive monoids. Our main result describes their equivariant cohomology in terms of…
The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier--Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a…
We present a new approach to the proof of ergodic theorems for actions of free groups based on geometric covering and asymptotic invariance arguments. Our approach can be viewed as a direct generalization of the classical geometric covering…
In the first part of the paper the natural scheme for proving noncommutative individual ergodic theorems for multiple sequences is described and applied to obtain results on unrestricted convergence of multiaverages. In the second part…
A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients in a field $K$, whose determinant describes a smooth cubic in the projective plane. To each such matrix one can associate a group scheme over…
A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.
A brief exposition of the point of higher topos theory in (mathematical) physics, commissioned for the Encyclopedia of Mathematical Physics 2nd ed.
We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finite number of pieces that are either one-dimensional or almost…
This paper gives a foundation of log smooth deformation theory. We study the infinitesimal liftings of log smooth morphisms and show that the log smooth deformation functor has a representable hull. This deformation theory gives, for…
In this paper The Ergodic Hypothesis is proven for one class of functions defined in the infinite dimensional unite cube where is given an action of some semigroup of mappings without the condition on metric transitivity. The result has not…