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Scaling laws in dynamical systems

Leonel, Edson Denis.

Scaling laws in dynamical systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Scaling laws in dynamical systemsby Edson Denis Leonel.
Author:	Leonel, Edson Denis.
Published:	Singapore :Springer Singapore :2021.
Description:	xxvii, 247 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Scaling laws (Statistical physics)
Online resource:	https://doi.org/10.1007/978-981-16-3544-1
ISBN:	9789811635441

Scaling laws in dynamical systems
Leonel, Edson Denis.

Scaling laws in dynamical systems[electronic resource] /by Edson Denis Leonel. - Singapore :Springer Singapore :2021. - xxvii, 247 p. :ill., digital ;24 cm. - Nonlinear physical science,1867-8459. - Nonlinear physical science..

Introduction -- One-dimensional mappings -- Some dynamical properties for the logistic map -- The logistic-like map -- Introduction to two dimensional mappings -- A Fermi accelerator model -- Dissipation in the Fermi-Ulam model -- Dynamical properties for a bouncer model -- Localization of invariant spanning curves -- Chaotic diffusion in non-dissipative mappings -- Scaling on a dissipative standard mapping -- Introduction to billiards dynamics -- Time dependent billiards -- Suppression of Fermi acceleration in the oval billiard -- A thermodynamic model for time dependent billiards.

This book discusses many of the common scaling properties observed in some nonlinear dynamical systems mostly described by mappings. The unpredictability of the time evolution of two nearby initial conditions in the phase space together with the exponential divergence from each other as time goes by lead to the concept of chaos. Some of the observables in nonlinear systems exhibit characteristics of scaling invariance being then described via scaling laws. From the variation of control parameters, physical observables in the phase space may be characterized by using power laws that many times yield into universal behavior. The application of such a formalism has been well accepted in the scientific community of nonlinear dynamics. Therefore I had in mind when writing this book was to bring together few of the research results in nonlinear systems using scaling formalism that could treated either in under-graduation as well as in the post graduation in the several exact programs but no earlier requirements were needed from the students unless the basic physics and mathematics. At the same time, the book must be original enough to contribute to the existing literature but with no excessive superposition of the topics already dealt with in other text books. The majority of the Chapters present a list of exercises. Some of them are analytic and others are numeric with few presenting some degree of computational complexity.

ISBN: 9789811635441

Standard No.: 10.1007/978-981-16-3544-1doiSubjects--Topical Terms:

190008
Scaling laws (Statistical physics)

LC Class. No.: QC174.85.S34 / L46 2021

Dewey Class. No.: 530.1595

Scaling laws in dynamical systems
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505 0 $a Introduction -- One-dimensional mappings -- Some dynamical properties for the logistic map -- The logistic-like map -- Introduction to two dimensional mappings -- A Fermi accelerator model -- Dissipation in the Fermi-Ulam model -- Dynamical properties for a bouncer model -- Localization of invariant spanning curves -- Chaotic diffusion in non-dissipative mappings -- Scaling on a dissipative standard mapping -- Introduction to billiards dynamics -- Time dependent billiards -- Suppression of Fermi acceleration in the oval billiard -- A thermodynamic model for time dependent billiards.
520 $a This book discusses many of the common scaling properties observed in some nonlinear dynamical systems mostly described by mappings. The unpredictability of the time evolution of two nearby initial conditions in the phase space together with the exponential divergence from each other as time goes by lead to the concept of chaos. Some of the observables in nonlinear systems exhibit characteristics of scaling invariance being then described via scaling laws. From the variation of control parameters, physical observables in the phase space may be characterized by using power laws that many times yield into universal behavior. The application of such a formalism has been well accepted in the scientific community of nonlinear dynamics. Therefore I had in mind when writing this book was to bring together few of the research results in nonlinear systems using scaling formalism that could treated either in under-graduation as well as in the post graduation in the several exact programs but no earlier requirements were needed from the students unless the basic physics and mathematics. At the same time, the book must be original enough to contribute to the existing literature but with no excessive superposition of the topics already dealt with in other text books. The majority of the Chapters present a list of exercises. Some of them are analytic and others are numeric with few presenting some degree of computational complexity.
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