scholarly journals On the number of ergodic measures for minimal shifts with eventually constant complexity growth

2016 ◽  
Vol 37 (7) ◽  
pp. 2099-2130
Author(s):  
MICHAEL DAMRON ◽  
JON FICKENSCHER
Keyword(s):  
Symbolic Dynamics ◽  
Explicit Description ◽  
Probability Measures ◽  
Bounded Number ◽  
Ergodic Measures ◽  
The One ◽  
Constant Growth ◽  
Block Growth ◽  
Linear Block

In 1985, Boshernitzan showed that a minimal (sub)shift satisfying a linear block growth condition must have a bounded number of ergodic probability measures. Recently, this bound was shown to be sharp through examples constructed by Cyr and Kra. In this paper, we show that under the stronger assumption of eventually constant growth, an improved bound exists. To this end, we introduce special Rauzy graphs. Variants of the well-known Rauzy graphs from symbolic dynamics, these graphs provide an explicit description of how a Rauzy graph for words of length $n$ relates to the one for words of length $n+1$ for each $n=1,2,3,\ldots \,$.

scholarly journals The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms

2020 ◽  
pp. 1-26
Author(s):  
SNIR BEN OVADIA
Keyword(s):  
Symbolic Dynamics ◽  
Full Measure ◽  
Probability Measures ◽  
Positive Entropy ◽  
Surface Diffeomorphisms ◽  
Srb Measures ◽  
Hyperbolic Diffeomorphisms ◽  
Set Of Points ◽  
Math Phys ◽  
Homoclinic Classes

Abstract The papers [O. M. Sarig. Symbolic dynamics for surface diffeomorphisms with positive entropy. J. Amer. Math. Soc.26(2) (2013), 341–426] and [S. Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. J. Mod. Dyn.13 (2018), 43–113] constructed symbolic dynamics for the restriction of $C^r$ diffeomorphisms to a set $M'$ with full measure for all sufficiently hyperbolic ergodic invariant probability measures, but the set $M'$ was not identified there. We improve the construction in a way that enables $M'$ to be identified explicitly. One application is the coding of infinite conservative measures on the homoclinic classes of Rodriguez-Hertz et al. [Uniqueness of SRB measures for transitive diffeomorphisms on surfaces. Comm. Math. Phys.306(1) (2011), 35–49].

Hyperimaginaries and automorphism groups

2001 ◽  
Vol 66 (1) ◽  
pp. 127-143 ◽  
Author(s):  
D. Lascar ◽  
A. Pillay
Keyword(s):  
Equivalence Relation ◽  
Galois Theory ◽  
Automorphism Groups ◽  
Infinite Length ◽  
Abstract Group ◽  
Simple Theories ◽  
Bounded Number ◽  
Compact Topology ◽  
The One ◽  
Number Of Classes

A hyperimaginary is an equivalence class of a type-definable equivalence relation on tuples of possibly infinite length. The notion was recently introduced in [1], mainly with reference to simple theories. It was pointed out there how hyperimaginaries still remain in a sense within the domain of first order logic. In this paper we are concerned with several issues: on the one hand, various levels of complexity of hyperimaginaries, and when hyperimaginaries can be reduced to simpler hyperimaginaries. On the other hand the issue of what information about hyperimaginaries in a saturated structure M can be obtained from the abstract group Aut(M).In Section 2 we show that if T is simple and canonical bases of Lascar strong types exist in Meq then hyperimaginaries can be eliminated in favour of sequences of ordinary imaginaries. In Section 3, given a type-definable equivalence relation with a bounded number of classes, we show how the quotient space can be equipped with a certain compact topology. In Section 4 we study a certain group introduced in [5], which we call the Galois group of T, develop a Galois theory and make the connection with the ideas in Section 3. We also give some applications, making use of the structure of compact groups. One of these applications states roughly that bounded hyperimaginaries can be eliminated in favour of sequences of finitary hyperimaginaries. In Sections 3 and 4 there is some overlap with parts of Hrushovski's paper [2].

Local dimension of ergodic measures for two-dimensional Lorenz transformations

2000 ◽  
Vol 20 (3) ◽  
pp. 911-923 ◽  
Author(s):  
THOMAS STEINBERGER
Keyword(s):  
Probability Measures ◽  
Two Dimensional ◽  
Poincaré Section ◽  
Poincare Section ◽  
Local Dimension ◽  
Lorenz Equation ◽  
Characteristic Exponents ◽  
Ergodic Measures

A class of transformations on $[0,1]^2$, which includes transformations obtained by a Poincaré section of the Lorenz equation, is considered. We prove a formula which connects local dimension, entropy and characteristic exponents of ergodic invariant probability measures.

scholarly journals TI in the Institutional Scientific Productivity of Ecuador, Cuba and Colombia

SIASAT ◽  
2022 ◽  
Vol 7 (1) ◽  
pp. 28-39
Author(s):  
Lisbet Eunice Pérez Anzardo ◽  
Rodolfo González Ortega ◽  
Pedro Bruzón Sosa ◽  
Catia Ruiz Bosch
Keyword(s):  
Social Development ◽  
Institutional Environment ◽  
Scientific Productivity ◽  
Scientific Production ◽  
Scientific Investigation ◽  
The Government ◽  
The One ◽  
The University ◽  
Constant Growth ◽  
Institutional Productivity

Scientific production is one of the indicators of relevance to measure the efficiency in the institutional environment, which implies a development conditioned in all the sectors from the society to world level. In the same way, the technologies of the information (TI) represent a decisive element for their administration which has experienced a constant growth during the last decades similar to the consolidation of the university studies in the different areas of the knowledge and study modalities. The following article makes a reflection on the base of the concepts and tendencies of the scientific investigation and its linking with the technologies of the information. The production of the investigation was characterized in the countries of Ecuador, Cuba and Colombia, as well as the existent relationship among the investment in technologies of the information and the institutional productivity, which was performed with the analysis of bibliometric indicatives. As a result, it was set down the bases for the theoretical-practical deeping of the investigation. Also, it was verified that the investment in IT focused in articles and scientific magazines, contribute to a better knowledge in academic institutions and that the three countries develop policies to motivate this activity, being Colombia the one with more production in the last ten years, as well as the one that has had bigger expense in IT as percentage of the GDP, which is carried out mainly by the government; although the administration of the knowledge has a transcendental impact for the economic and social development of any country.   

STATIONARY WEAK SOLUTIONS FOR STOCHASTIC 3D NAVIER–STOKES EQUATIONS WITH LÉVY NOISE

2012 ◽  
Vol 12 (01) ◽  
pp. 1150006 ◽  
Author(s):  
ZHAO DONG ◽  
WENBO V. LI ◽  
JIANLIANG ZHAI
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lévy Noise ◽  
Probability Measures ◽  
Stationary Probability ◽  
Navier Stokes Equations ◽  
Wiener Processes ◽  
The One ◽  
Levy Noise

We first study the existence of stationary weak solutions of stochastic 3D Navier–Stokes equations involving jumps, and the associated Galerkin stationary probability measures for this case. Then we present a comparison between the Galerkin stationary probability measures for the case driven by Lévy noise and the one driven by Wiener processes.

scholarly journals Distortion risk measures, ROC curves, and distortion divergence

2018 ◽  
Vol 35 (1-2) ◽  
pp. 35-50
Author(s):  
Johannes M. Schumacher
Keyword(s):  
Operating Characteristic ◽  
Risk Measures ◽  
Roc Curves ◽  
Probability Measures ◽  
Distortion Functions ◽  
Simple Alternative ◽  
Measures Of Risk ◽  
New Interpretation ◽  
The One ◽  
Distortion Risk Measures

AbstractDistortion functions are employed to define measures of risk. Receiver operating characteristic (ROC) curves are used to describe the performance of parametrized test families in testing a simple null hypothesis against a simple alternative. This paper provides a connection between distortion functions on the one hand, and ROC curves on the other. This leads to a new interpretation of some well-known classes of distortion risk measures, and to a new notion of divergence between probability measures.

scholarly journals Invariant measures on stationary Bratteli diagrams

2009 ◽  
Vol 30 (4) ◽  
pp. 973-1007 ◽  
Author(s):  
S. BEZUGLYI ◽  
J. KWIATKOWSKI ◽  
K. MEDYNETS ◽  
B. SOLOMYAK
Keyword(s):  
Dynamical Systems ◽  
Equivalence Relation ◽  
Complex Number ◽  
Incidence Matrix ◽  
Invariant Measures ◽  
Explicit Description ◽  
Bratteli Diagram ◽  
Probability Measures ◽  
Bratteli Diagrams ◽  
Substitution Dynamical Systems

AbstractWe study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we give an explicit description of all ergodic probability measures that are invariant with respect to the tail equivalence relation (or the Vershik map); these measures are completely described by the incidence matrix of the Bratteli diagram. Since such diagrams correspond to substitution dynamical systems, our description provides an algorithm for finding invariant probability measures for aperiodic non-minimal substitution systems. Several corollaries of these results are obtained. In particular, we show that the invariant measures are not mixing and give a criterion for a complex number to be an eigenvalue for the Vershik map.

scholarly journals Infinite interval exchange transformations from shifts

2016 ◽  
Vol 37 (6) ◽  
pp. 1935-1965 ◽  
Author(s):  
LUIS-MIGUEL LOPEZ ◽  
PHILIPPE NARBEL
Keyword(s):  
Topological Entropy ◽  
Interval Exchange ◽  
Infinite Interval ◽  
Linear Factor ◽  
Interval Exchange Transformations ◽  
Interval Exchanges ◽  
Finiteness Properties ◽  
Block Growth ◽  
Linear Block

We show that minimal shifts with zero topological entropy are topologically conjugate to interval exchange transformations, which are generally infinite. When these shifts have linear factor complexity (linear block growth), the conjugate interval exchanges are proved to satisfy strong finiteness properties.

scholarly journals A Sustainable Niche Market: How Does Honey Behave?

2020 ◽  
Vol 12 (24) ◽  
pp. 10678
Author(s):  
Liam Pippinato ◽  
Simone Blanc ◽  
Teresina Mancuso ◽  
Filippo Brun
Keyword(s):  
Significant Influence ◽  
Cultural Distance ◽  
Gravity Models ◽  
Food Sector ◽  
Niche Market ◽  
The World ◽  
Standards And Regulations ◽  
Econometric Methodology ◽  
The One ◽  
Constant Growth

The global honey market has witnessed constant growth over recent decades, especially in Asian regions. In recent years, the increase in export flows of this product throughout the world has raised the issue of the lack of international import standards and regulations, making trade susceptible to variables that are not only economic, but also social or political. The objective of this study is therefore to explore, using the econometric methodology of gravity models, what the determinants of the international honey trade are, both economic and socio-cultural, and to verify whether a niche market, such as the one being examined, is influenced by these covariates, in a similar manner to the main commodities of the agri-food sector, or if honey displays a unique behavior. The results show that honey market behavior is not statistically different from that of the main agri-food products already studied and that the cultural distance, introduced as a covariate, does not have a significant influence.

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