scholarly journals On the bialgebra of functional graphs and differential algebras

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Maurice Ginocchio
Keyword(s):  
Dynamical Systems ◽  
Differential Operators ◽  
Discrete Dynamical Systems ◽  
Rooted Trees ◽  
Connected Components ◽  
Differential Algebras ◽  
Noncommutative Polynomials ◽  
International Audience

International audience We develop the bialgebraic structure based on the set of functional graphs, which generalize the case of the forests of rooted trees. We use noncommutative polynomials as generating monomials of the functional graphs, and we introduce circular and arborescent brackets in accordance with the decomposition in connected components of the graph of a mapping of \1, 2, \ldots, n\ in itself as in the frame of the discrete dynamical systems. We give applications fordifferential algebras and algebras of differential operators.

scholarly journals Sur le retard à la bifurcation

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Augustin Fruchard ◽  
Reinhard Schäfke
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Discrete Dynamical Systems ◽  
International Audience ◽  
Bifurcation Delay

International audience We give a non-exhaustive overview of the problem of bifurcation delay from its appearance in France at the end of the 80ies to the most recent contributions. We present the bifurcation delay for differential equations as well as for discrete dynamical systems. Nous donnons un aperçu non exhaustif du problème du retard à la bifurcation, depuis son apparition en France à la fin des années 1980 jusqu’aux contributions les plus récentes. Le problème et les résultats sont présentés d’une part pour les équations différentielles et d’autre part pour les systèmes dynamiques discrets

scholarly journals Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Edward G. Belaga ◽  
Maurice Mignotte
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Discrete Dynamical Systems ◽  
Experimental Results ◽  
Diophantine Representation ◽  
Random Behavior ◽  
International Audience ◽  
Collatz Problem

International audience Building on theoretical insights and rich experimental data of our preprints, we present here new theoretical and experimental results in three interrelated approaches to the Collatz problem and its generalizations: \emphalgorithmic decidability, random behavior, and Diophantine representation of related discrete dynamical systems, and their \emphcyclic and divergent properties.

scholarly journals Resonance in orbits of plane partitions

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Kevin Dilks ◽  
Oliver Pechenik ◽  
Jessica Striker
Keyword(s):  
Dynamical Systems ◽  
Discrete Dynamical Systems ◽  
Plane Partitions ◽  
Higher Dimensional ◽  
International Audience ◽  
K Promotion

International audience We introduce a new concept of resonance on discrete dynamical systems. Our main result is an equivariant bijection between plane partitions in a box under rowmotion and increasing tableaux under K-promotion, using a generalization of the equivariance of promotion and rowmotion [J. Striker–N. Williams '12] to higher dimensional lattices. This theorem implies new results for K-promotion and new proofs of previous results on plane partitions.

scholarly journals Hidden Attractors in Discrete Dynamical Systems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 616
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik
Keyword(s):  
Dynamical Systems ◽  
Chaos Theory ◽  
Scientific Literature ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Continuous Systems ◽  
Hidden Attractors ◽  
Negative Effects ◽  
Chemical Reactors ◽  
Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

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