Author: Jean-Louis CallotPublisher:
ISBN:
Category : Differential equations, Linear
Languages : fr
Pages : 101
Book Description
Bifurcations du portrait de phase pour des équations différentielles linéaires du second ordre ayant pour type l'équation d'Hermite
Author: Jean-Louis CallotPublisher:
ISBN:
Category : Differential equations, Linear
Languages : fr
Pages : 101
Book Description
Handbook of Geometry and Topology of Singularities VI: Foliations
Author: Felipe CanoPublisher: Springer Nature
ISBN: 3031541723
Category :
Languages : en
Pages : 500
Book Description
Neutrices and External Numbers
Author: Bruno DinisPublisher: CRC Press
ISBN: 1000012204
Category : Mathematics
Languages : en
Pages : 357
Book Description
Neutrices and External Numbers: A Flexible Number System introduces a new model of orders of magnitude and of error analysis, with particular emphasis on behaviour under algebraic operations. The model is formulated in terms of scalar neutrices and external numbers, in the form of an extension of the nonstandard set of real numbers. Many illustrative examples are given. The book starts with detailed presentation of the algebraic structure of external numbers, then deals with the generalized Dedekind completeness property, applications in analysis, domains of validity of approximations of solutions of differential equations, particularly singular perturbations. Finally, it describes the family of algebraic laws characterizing the practice of calculations with external numbers. Features Presents scalar neutrices and external numbers, a mathematical model of order of magnitude within the real number system. Outlines complete algebraic rules for the neutrices and external numbers Conducts operational analysis of convergence and integration of functions known up to orders of magnitude Formalises a calculus of error propagation, covariant with algebraic operations Presents mathematical models of phenomena incorporating their necessary imprecisions, in particular related to the Sorites paradox
Dynamic Bifurcations
Author: Eric BenoitPublisher: Springer
ISBN: 9783540549000
Category : Mathematics
Languages : en
Pages : 240
Book Description
Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambert: Finitely Differentiable Ducks and Finite Expansions.- G. Wallet: Overstability in Arbitrary Dimension.- F.Diener, M. Diener: Maximal Delay.- A. Fruchard: Existence of Bifurcation Delay: the Discrete Case.- C. Baesens: Noise Effect on Dynamic Bifurcations:the Case of a Period-doubling Cascade.- E. Benoit: Linear Dynamic Bifurcation with Noise.- A. Delcroix: A Tool for the Local Study of Slow-fast Vector Fields: the Zoom.- S.N. Samborski: Rivers from the Point ofView of the Qualitative Theory.- F. Blais: Asymptotic Expansions of Rivers.-I.P. van den Berg: Macroscopic Rivers
Memorandum from Institute of Economic Research, Faculty of Economics, University of Groningen
Author: Russian Mathematical Surveys
Author: Non Standard Analysis
Author: André PétryPublisher:
ISBN:
Category : Nonstandard mathematical analysis
Languages : fr
Pages : 160
Book Description
Recherches sur l'intégration des équations différentielles linéaires du second ordre
Author: J.-M. de TillyPublisher:
ISBN:
Category : Differential equations, Linear
Languages : fr
Pages : 98
Book Description
Note sur la première méthode de Brisson pour l'intégration des équations linéaires aux différences finies ou infiniment petites
Author: Paul MansionBifurcation and Nonlinear Eigenvalue Problems
Author: Claude BardosPublisher:
ISBN:
Category : Bifurcation theory
Languages : en
Pages : 312
Book Description