Related papers: Smooth ergodic theory
The Oseledets Multiplicative Ergodic theorem is a basic result with numerous applications throughout dynamical systems. These notes provide an introduction to this theorem, as well as subsequent generalizations. They are based on lectures…
The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.
This survey is a 2022 update of the 2008 version, with recent developments and new references.
We develop the intersection theory associated to immersed, oriented and mea- sured solenoids, which were introduced in arXiv:0910.2836.
The aim of this paper is to generalize Grothendieck's theory of smooth functors in order to include within this framework the theory of fibered categories. We obtain in particular a new characterization of fibered categories.
The survey presents the main developments obtained over the last decade regarding pointwise ergodic theorems for measure preserving actions of locally compact groups. The survey includes an exposition of the solutions to a number of long…
A rather general ergodic type scheme is presented on arbitrary sets X, as they are generated by arbitrary mappings T : X \longrightarrow X. The structures considered on X are given by suitable subsets of the set of all of its finite…
We provide an ergodic theory framework to study statistical properties of smooth sequences over the odd alphabet {1, 3}. The arithmetic nature of this alphabet yields a partition of the subshift of smooth sequences based on their local…
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.
This article aims at giving a general presentation of spintronics, an important field of research developing today along many new directions in physics of condensed matter. We tried to present simply the physical phenomena involved in…
Smooth K-functors are introduced and the smooth K-theory of locally convex algebras is developed. It is proved that the algebraic and smooth K-functors are isomorphic on the category of quasi stable real (or complex) Frechet algebras.
This paper presents a gentle and informal introduction to the Skorokhod topologies. Focus is on motivating examples and concepts.
This encyclopedia article briefly reviews without proofs some of the main results in symplectic reduction. The article recalls most the necessary prerequisites to understand the main results, namely, group actions, momentum maps, and…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.
In order to provide a good categorical setting to the many different spaces of fields arising in the description of physical theories, a pedagogical introduction to the categorical notion of smooth sets is provided and some simple…
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.
The purpose of this paper is to present a systematic exposition of the main results obtained in the studies carried out in groupoid theory. Key words and phrases: groupoid, topological groupoid, Lie groupoid, group-groupoid, vector…