3 edition of **Thermodynamic Formalism and Applications to Dimension Theory** found in the catalog.

- 326 Want to read
- 15 Currently reading

Published
**2011**
by Springer Basel AG in Basel
.

Written in English

- Mathematics,
- Differentiable dynamical systems

**Edition Notes**

Statement | by Luis Barreira |

Series | Progress in Mathematics -- 294 |

Contributions | SpringerLink (Online service) |

The Physical Object | |
---|---|

Format | [electronic resource] / |

ID Numbers | |

Open Library | OL25567950M |

ISBN 10 | 9783034802055, 9783034802062 |

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and properties of behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical. Physica D 50 () North-Holland Thermodynamic formalism for quantum-mechanical systems Christian Beck Institut f Theoretische Physik, RWTH, W Aachen, Germany Received 1 September Revised manuscript received 8 January Accepted 9 January Communicated by H. Flaschka Based on the thermodynamic formalism of dynamical systems I .

The idea of this theory is to generalize classical results on thermodynamic formalism replacing the pressure of a continuous function with the pressure of a sequence of continuous functions. It was Falconer [F1] who introduced this set of ideas with the purpose of studying dimension theory of non-conformal systems. Thermodynamic formalism for a family of non-uniformly hyperbolic horseshoes and the unstable Jacobian. Ergodic Theory and Dynamical Systems, Vol. 31, Issue. 02, p. Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics, Vol. , Issue. 1, p. Dimension Theory. Princeton.

on the formalism and its applications. The book is divided roughly into four partsâ€”overview, statistical mechanics, information theory, and biological systems. It provides both the scope needed to show the central intellectual core of the formalism and the details required by specialists for narrow applications. were deﬂned in dimension theory and ergodic theory. It has been found out that the dimension of non-conformal repellers can be well estimated by the zero of pressure function (see e.g. [1, 2, 12, 13, 29]). Falconer ([13]) considered the thermodynamic formalism for .

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The book is probably best read by someone already familiar with the basics of ergodic theory, dynamical systems, and the Hausdorff dimension. the book gives the reader a good grounding in both thermodynamical formalism and applying the thermodynamic formalism to prove results in the dimension theory of dynamical systems.” (Thomas Michael Cited by: This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis Thermodynamic Formalism and Applications to Dimension Theory | SpringerLink Skip to main content Skip to table of contents.

This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems.

This book is dedicated to the thermodynamic formalism, its extensions, and its applications, with emphasis on the study of the relation to dimension theory and multifractal analysis of dynamical. Search for books, ebooks, and physical Thermodynamic Formalism and Applications to Dimension Theory.

Bibliographic Details; Format: Book: Language: English: Thermodynamic formalism and applications to dimension theory by: Barreira, Luis, Published: () Dimension.

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Request PDF | A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems | A non-additive version of the thermodynamic formalism. July Organisers: Oliver Jenkinson, Thomas Jordan, Anders Öberg, Richard Sharp, Daniel Thompson The last decade has seen spectacular and continuing advances in an approach to ergodic theory and its applications using the techniques and tools of thermodynamic aim of this workshop is to progress this theory by focusing on a number of outstanding problems and.

Thermodynamic Formalism and Applications to Dimension Theory. For further developments of the thermodynamic formalism we refer to the books [,]. () Thermodynamic Formalism: Basic Notions. In: Thermodynamic Formalism and Applications to Dimension Theory. Progress in Mathematics, vol Springer, Basel.

First. A Non-Additive Thermodynamic Formalism and Applications to Dimension Theory of Hyperbolic Dynamical Systems () Cached. {Barreira96anon-additive, author = {Luis M. Barreira}, title = {A Non-Additive Thermodynamic Formalism and Applications to Dimension Theory of Hyperbolic Dynamical Systems}, journal = {}, year = { }.

Bowen Equilibrium states and the Ergodic theory of Anosov diffeomomorphisms Springer-Verlag LNMHeidelberg, D. Ruelle Thermodynamic formalism, Cambridge Mathematical Library, Cambridge University Press, Cambridge, O.

Sarig Lecture notes on Thermodynamic formalism for topological Markov shifts Penn State, Spring This volume provides a unified exposition of thermodynamic formalism and some of its main extensions, with an emphasis on the relation to the dimension theory and the multifractal analysis of dynamical systems.

It also includes a discussion of the most substantial applications. Barreira, Thermodynamic Formalism and Applications to Dimension Theory, Progress in Mathematics (Birkhäuser, ).

Crossref, Google Scholar R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics (Springer-Verlag. For the mathematical theory of multifractal formalism and its relation to thermodynamic formalism, we recommend.

In this article we extend the multifractal formalism for local dimension spectra of Gibbs measures supported on the attractor Λ ⊂ R of a conformal iterated function system on the real line. This workshop will be focused on Thermodynamic Formalism and its applications.

It will deal both with recent developments in the field and also its applications. It is a feature of this area that it has many applications to related fields, such as hyperbolic geometry and fractal geometry.

His main research area is Thermodynamic Formalism. He is particularly interested in applications to other areas of mathematics, including geometry, number theory, dimension theory and analysis. A PhD graduate from Bologna, Sandro Vaienti is.

Thermodynamic formalism (TF) is a very exciting area which still to these days remains quite active. One of the most prominent applications of TF is fractal geometry. On of the most amazing results in my opinion, is Bowen's formula, which he derived to study the dimension of quasi-circles but it was then generalized to a more general setting.

Thermodynamic Formalism and Applications to Dimension Theory - Luis Barreira - Free ebook download as PDF File .pdf), Text File .txt) or read book online for free.

Formalismo termodinámico. A Synopsis of Classical Thermodynamics. Single component Fluid – Fundamentals. Single Component Fluid – Applications. Homogeneous (Single Phase) Mixtures. Heterogeneous (Multiphase) Mixtures. Reaction Equilibrium. The book presents the concepts and equations of equilibrium thermodynamics or thermostatics in a logical and.

Singular perturbation of symbolic dynamics via thermodynamic formalism - Volume 28 Issue 4 - TAKEHIKO MORITA, HARUYOSHI TANAKA.

Dimension Theory in Dynamical Systems: Comtemporary Views and Applications. The University of Chicago Press, Chicago, [13] Ruelle, D. a one-dimensional model, but performs much better in dimension three. Andrej Kolmogorov (), Russian probabilist and founding father of er-godic theory in Russia.

His de niton of entropy paved the way for the current mathematical approach to thermodynamic formalism.9. Application III: Dimension spectra 26 References 28 1. Introduction The point of departure for this survey is the nonadditive thermodynamic formalism developed in [1], having in mind certain applications to the di-mension theory of dynamical systems, as detailed below.

Our main aim is.THERMODYNAMIC FORMALISM AND GEOMETRIC APPLICATIONS FOR Estimates for the hyperbolic dimension 25 Bowen’s Formula 26 7. Real Analyticity of Fractal Dimensions 27 8.

Beyondhyperbolicity 30 Originating from statistical physics, the dynamical theory of thermodynamic .