scholarly journals Συναρτησιοαναλυτικές μέθοδοι σε μη γραμμικά στάσιμα και εξελικτικά προβλήματα

2007 ◽  
Author(s):  
Μαρία-Ελένη Πούλου
Keyword(s):  
Spectral Analysis ◽  
Dynamical Systems ◽  
Variational Methods ◽  
Systems Theory ◽  
Global Attractor ◽  
Sobolev Spaces ◽  
Topological Degree ◽  
Dynamical Systems Theory ◽  
Klein Gordon

Η εργασία αυτή μελετά μη-γραμμικά στάσιμα και εξελικτικά προβλήματα κάνοντας χρήση μεθόδων της Συναρτησιακής Ανάλυσης. Λόγω της εκφυλισμένης φύσης των εξισώσεων αλλά και της ύπαρξης μη συμπαγών τελεστών για τη μελέτη των στάσιμων προβλημάτων χρησιμοποιούνται Χώροι Lebesque και Sobolev με Βάρος (Weighted Lebesque and Sobolev Spaces). Για τα μεν στάσιμα προβλήματα, στόχος είναι η απόδειξη ύπαρξης πρωτεύοντος ιδιοζεύγους χρησιμοποιώντας μεταβολικές και άλλες μεθόδους της Φασματικής Ανάλυσης (spectral analysis) καθώς και η απόδειξη ύπαρξης 'θετικού κλάδου Τοπικής και Ολικής Διακλάδωσης με τη βοήθεια των μεταβολικών μεθόδων (variational methods) και της Θεωρίας Τοπολογικού Βαθμού (topological degree). Στη συνέχεια η μελέτη επεκτείνεται σε εξελικτικά προβλήματα, όπου στόχο αποτελεί η απόδειξη ύπαρξης και μοναδικότητας ολικής λύσης για ένα εξελικτικό σύστημα τύπου Klein-Gordon-Schrödinger και η απόδειξη ύπαρξης ενός συμπαγούς, αναλλοίωτου υποσύνολου του χώρου φάσεων (ολικός ελκυστής) (Global Attractor), το οποίο έλκει ομοιόμορφα όλες τις τροχιές, για δεδομένες αρχικές συνθήκες σε ένα φραγμένο σύνολο με τη βοήθεια της Θεωρίας των Απειροδιάστατων Δυναμικών Συστημάτων (Dynamical Systems Theory). […]

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

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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