Attractors for dynamical systems in topological spaces

Abstract While neural networks are highly effective at learning task-relevant representations from data, they typically do not learn representations with the kind of symbolic structure that is hypothesized to support high-level cognitive processes, nor do they naturally model such structures within problem domains that are continuous in space and time. To fill these gaps, this work exploits a method for defining vector representations that bind discrete (symbol-like) entities to points in continuous topological spaces in order to simulate and predict the behavior of a range of dynamical systems. These vector representations are spatial semantic pointers (SSPs), and we demonstrate that they can (1) be used to model dynamical systems involving multiple objects represented in a symbol-like manner and (2) be integrated with deep neural networks to predict the future of physical trajectories. These results help unify what have traditionally appeared to be disparate approaches in machine learning.

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Neutrosophic Orbit Topological Spaces

Trends in Sciences ◽

10.48048/tis.2021.1443 ◽

2021 ◽

Vol 18 (24) ◽

pp. 1443

Author(s):

T Madhumathi ◽

F NirmalaIrudayam

Keyword(s):

Dynamical System ◽

Dynamical Systems ◽

Topological Space ◽

Necessary Conditions ◽

Neutrosophic Set ◽

Topological Spaces ◽

Open Set ◽

Evolution Function

Neutrosophy is a flourishing arena which conceptualizes the notion of true, falsity and indeterminancy attributes of an event. In the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. Hence in this paper we focus on introducing the concept of neutrosophic orbit topological space denoted as (X, tNO). Also, some of the important characteristics of neutrosophic orbit open sets are discussed with suitable examples. HIGHLIGHTS The orbit in mathematics has an important role in the study of dynamical systems Neutrosophy is a flourishing arena which conceptualizes the notion of true, falsity and indeterminancy attributes of an event. We combine the above two topics and create the following new concept The collection of all neutrosophic orbit open sets under the mapping . we introduce the necessary conditions on the mapping 𝒇 in order to obtain a fixed orbit of a neutrosophic set (i.e., 𝒇(𝝁) = 𝝁) for any neutrosophic orbit open set 𝝁 under the mapping 𝒇

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Discrete dynamical systems in L-topological spaces

Fuzzy Sets and Systems ◽

10.1016/j.fss.2005.05.026 ◽

2005 ◽

Vol 156 (1) ◽

pp. 25-42 ◽

Cited By ~ 2

Author(s):

Li Chen ◽

Hui Kou ◽

Mao-Kang Luo ◽

Weinian Zhang

Keyword(s):

Dynamical Systems ◽

Discrete Dynamical Systems ◽

Topological Spaces

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On Baire generalized topological spaces and some problems connected with discrete dynamical systems

Traditional and present-day topics in real analysis. Dedicated to Professor Jan Stanisław Lipiński ◽

10.18778/7525-971-1.11 ◽

2013 ◽

pp. 151-172

Author(s):

Anna Loranty ◽

Ryszard J. Pawlak

Keyword(s):

Dynamical Systems ◽

Discrete Dynamical Systems ◽

Topological Spaces

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Schreier graphs of spinal groups

International Journal of Algebra and Computation ◽

10.1142/s0218196721400099 ◽

2021 ◽

pp. 1-26

Author(s):

Tatiana Nagnibeda ◽

Aitor Pérez

Keyword(s):

Dynamical Systems ◽

Rooted Trees ◽

Topological Spaces ◽

Geometric Properties ◽

Intermediate Growth ◽

Isomorphism Classes ◽

Schreier Graphs ◽

Number Of Ends

We study Schreier dynamical systems associated with a vast family of groups that hosts many known examples of groups of intermediate growth. We are interested in the orbital graphs for the actions of these groups on [Formula: see text]-regular rooted trees and on their boundaries, viewed as topological spaces or as spaces with measure. They form interesting families of finitely ramified graphs, and we study their combinatorics, their isomorphism classes and their geometric properties, such as growth and the number of ends.

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