On Factor Maps that Send Markov Measures to Gibbs Measures

2010 ◽  
Vol 141 (6) ◽  
pp. 1055-1070 ◽  
Author(s):  
Jisang Yoo
Keyword(s):  
Gibbs Measures ◽  
Markov Measures ◽  
Factor Maps

scholarly journals Sequential Gibbs Measures and Factor Maps

2018 ◽  
Vol 172 (3) ◽  
pp. 833-853
Author(s):  
Giovane Ferreira ◽  
Krerley Oliveira
Keyword(s):  
Gibbs Measures ◽  
Factor Maps

scholarly journals On Gibbs Measures and Spectra of Ruelle Transfer Operators

2017 ◽  
Vol 60 (2) ◽  
pp. 411-421
Author(s):  
Luchezar Stoyanov
Keyword(s):  
Spectral Radius ◽  
Spectral Properties ◽  
Gibbs Measures ◽  
Transfer Operator ◽  
Frobenius Theorem ◽  
Transfer Operators

AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.

scholarly journals Regional Analyses of Rainfall-Induced Landslide Initiation in Upper Gudbrandsdalen (South-Eastern Norway) Using TRIGRS Model

Geosciences ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 35
Author(s):  
Luca Schilirò ◽  
José Cepeda ◽  
Graziella Devoli ◽  
Luca Piciullo
Keyword(s):  
Numerical Simulations ◽  
Regional Scale ◽  
Shallow Landslides ◽  
South Eastern ◽  
Physically Based ◽  
Triggering Conditions ◽  
Cover Thickness ◽  
Regional Analyses ◽  
Factor Maps ◽  
Eastern Norway

In Norway, shallow landslides are generally triggered by intense rainfall and/or snowmelt events. However, the interaction of hydrometeorological processes (e.g., precipitation and snowmelt) acting at different time scales, and the local variations of the terrain conditions (e.g., thickness of the surficial cover) are complex and often unknown. With the aim of better defining the triggering conditions of shallow landslides at a regional scale we used the physically based model TRIGRS (Transient Rainfall Infiltration and Grid-based Regional Slope stability) in an area located in upper Gudbrandsdalen valley in South-Eastern Norway. We performed numerical simulations to reconstruct two scenarios that triggered many landslides in the study area on 10 June 2011 and 22 May 2013. A large part of the work was dedicated to the parameterization of the numerical model. The initial soil-hydraulic conditions and the spatial variation of the surficial cover thickness have been evaluated applying different methods. To fully evaluate the accuracy of the model, ROC (Receiver Operating Characteristic) curves have been obtained comparing the safety factor maps with the source areas in the two periods of analysis. The results of the numerical simulations show the high susceptibility of the study area to the occurrence of shallow landslides and emphasize the importance of a proper model calibration for improving the reliability.

scholarly journals PHASE TRANSITIONS AND QUANTUM STABILIZATION IN QUANTUM ANHARMONIC CRYSTALS

2008 ◽  
Vol 20 (05) ◽  
pp. 529-595 ◽  
Author(s):  
ALINA KARGOL ◽  
YURI KONDRATIEV ◽  
YURI KOZITSKY
Keyword(s):  
Phase Transitions ◽  
Gibbs Measures ◽  
Quantum Effects ◽  
Gibbs States ◽  
Translation Invariance ◽  
Unified Theory ◽  
The Relationship ◽  
Anharmonic Crystals

A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs states in terms of path measures (Euclidean Gibbs measures). It covers the case of crystals without translation invariance, as well as the case of asymmetric anharmonic potentials. The results obtained are compared with those known in the literature.

ALMOST ADDITIVE THERMODYNAMIC FORMALISM: SOME RECENT DEVELOPMENTS

2010 ◽  
Vol 22 (10) ◽  
pp. 1147-1179 ◽  
Author(s):  
LUIS BARREIRA
Keyword(s):  
Variational Principle ◽  
Existence And Uniqueness ◽  
Gibbs Measures ◽  
Thermodynamic Formalism ◽  
Topological Pressure ◽  
Present Stage ◽  
The Past ◽  
Recent Developments ◽  
General Sequences ◽  
Uniqueness Of Equilibrium

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning, for example, a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures (at least without further restrictive assumptions). On the other hand, in the case of almost additive sequences, it is possible to establish a variational principle and to discuss the existence and uniqueness of equilibrium and Gibbs measures, among several other results. After presenting in a self-contained manner the foundations of the theory, the survey includes the description of three applications of the almost additive thermodynamic formalism: a multifractal analysis of Lyapunov exponents for a class of nonconformal repellers; a conditional variational principle for limits of almost additive sequences; and the study of dimension spectra that consider simultaneously limits into the future and into the past.

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