scholarly journals Some elements for a history of the dynamical systems theory

2021 ◽  
Vol 31 (5) ◽  
pp. 053110
Author(s):  
Christophe Letellier ◽  
Ralph Abraham ◽  
Dima L. Shepelyansky ◽  
Otto E. Rössler ◽  
Philip Holmes ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Dynamical Systems Theory ◽  
History Of

The Oxford Handbook of Generality in Mathematics and the Sciences

2017 ◽  
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Mathematical Physics ◽  
Dynamical Systems Theory ◽  
Evolutionary Strategies ◽  
René Descartes ◽  
History Of ◽  
Recurrence Theorem ◽  
Different Levels

This handbook examines how actors have valued generality in mathematics and the sciences and how they worked with specific types of “general” entities, procedures, and arguments. It argues that actors have shaped these various types of generality, mainly by introducing specific terminologies to distinguish between different levels or forms of generality, as well as designing means to work with them, or to work in relation to them. The book is organized into three parts. Part I deals with the meaning and value of generality, and more specifically the value of generality in Michel Chasles’s historiography of geometry and generality in Gottfried Leibniz’s mathematics. Part II focuses on statements and concepts that make up the general, covering topics such as Henri Poincaré’s work on the recurrence theorem and the role of genericity in the history of dynamical systems theory. Part III explores the practices of generality, including the dispute over tangents between René Descartes and Pierre de Fermat, generality in James Clerk Maxwell’s theory of electromagnetism, and practices of generalization in mathematical physics, biology, and evolutionary strategies.

The role of genericity in the history of dynamical systems theory

2017 ◽  
Author(s):  
Tatiana Roque
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Systems Theory ◽  
Singularity Theory ◽  
Dynamical Systems Theory ◽  
Henri Poincaré ◽  
New Methods ◽  
History Of ◽  
Equation Différentielle

This article examines the role of genericity in the development of dynamical systems theory. In his memoir ‘Sur les courbes définies par une équation différentielle’, published in four parts between 1881 and 1886, Henri Poincaré studied the behavior of curves that are solutions for certain types of differential equations. He successfully classified them by focusing on singular points, described the trajectories’ behavior in important particular cases and provided new methods that proved to be extremely useful. This article begins with a discussion of singularity theory and its influence on the first definitions of genericity, along with the application of the notions of structural stability and genericity to understand dynamical systems. It also analyzes the Smale conjecture and how it was proven wrong and concludes with an overview of changes in the definitions of genericity meant to describe the ‘dark realm of dynamics’.

scholarly journals The Dynamics of Musical Participation

2021 ◽  
pp. 102986492098831
Author(s):  
Andrea Schiavio ◽  
Pieter-Jan Maes ◽  
Dylan van der Schyff
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Dynamical Systems Theory ◽  
Coordination Dynamics ◽  
Musical Experience ◽  
The Core ◽  
Interactive Dynamics ◽  
Interdisciplinary Scholarship ◽  
Core Features

In this paper we argue that our comprehension of musical participation—the complex network of interactive dynamics involved in collaborative musical experience—can benefit from an analysis inspired by the existing frameworks of dynamical systems theory and coordination dynamics. These approaches can offer novel theoretical tools to help music researchers describe a number of central aspects of joint musical experience in greater detail, such as prediction, adaptivity, social cohesion, reciprocity, and reward. While most musicians involved in collective forms of musicking already have some familiarity with these terms and their associated experiences, we currently lack an analytical vocabulary to approach them in a more targeted way. To fill this gap, we adopt insights from these frameworks to suggest that musical participation may be advantageously characterized as an open, non-equilibrium, dynamical system. In particular, we suggest that research informed by dynamical systems theory might stimulate new interdisciplinary scholarship at the crossroads of musicology, psychology, philosophy, and cognitive (neuro)science, pointing toward new understandings of the core features of musical participation.

scholarly journals Coevolving institutions and the paradox of informal constraints

2021 ◽  
pp. 1-20
Author(s):  
Daniel Seligson ◽  
Anne E. C. McCants
Keyword(s):  
Economic Growth ◽  
Game Theory ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Institutional Economics ◽  
Dynamical Systems Theory ◽  
New Institutional Economics ◽  
Long Run

Abstract We can all agree that institutions matter, though as to which institutions matter most, and how much any of them matter, the matter is, paraphrasing Douglass North's words at the Nobel podium, unresolved after seven decades of immense effort. We suggest that the obstacle to progress is the paradigm of the New Institutional Economics itself. In this paper, we propose a new theory that is: grounded in institutions as coevolving sources of economic growth rather than as rules constraining growth; and deployed in dynamical systems theory rather than game theory. We show that with our approach some long-standing problems are resolved, in particular, the paradoxical and perplexingly pervasive influence of informal constraints on the long-run character of economies.

On the Roughness of Quasinilpotency Property of One-parameter Semigroups

2017 ◽  
Vol 60 (2) ◽  
pp. 364-371 ◽  
Author(s):  
Ciprian Preda
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Infinitesimal Generator ◽  
Autonomous Systems ◽  
Dynamical Systems Theory ◽  
Extinction Property ◽  
Quasinilpotent Operators ◽  
Strong Concept ◽  
Time Extinction

AbstractLet S := {S(t)}t≥0 be a C0-semigroup of quasinilpotent operators (i.e., σ(S(t)) = {0} for eacht> 0). In dynamical systems theory the above quasinilpotency property is equivalent to a very strong concept of stability for the solutions of autonomous systems. This concept is frequently called superstability and weakens the classical ûnite time extinction property (roughly speaking, disappearing solutions). We show that under some assumptions, the quasinilpotency, or equivalently, the superstability property of a C0-semigroup is preserved under the perturbations of its infinitesimal generator.

Information processing and dynamical systems approaches are complementary

2002 ◽  
Vol 25 (5) ◽  
pp. 639-640
Author(s):  
David Spurrett
Keyword(s):  
Information Processing ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Dynamical Systems Theory ◽  
Communication Studies ◽  
New Paradigm ◽  
Systems Approaches ◽  
False Dichotomy ◽  
Language Research ◽  
Ape Language

Shanker & King (S&K) trumpet the adoption of a “new paradigm” in communication studies, exemplified by ape language research. Though cautiously sympathetic, I maintain that their argument relies on a false dichotomy between “information” and “dynamical systems” theory, and that the resulting confusion prevents them from recognizing the main chance their line of thinking suggests.

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