TY - GEN

T1 - On a method of applied symbolic dynamics for investigation of dynamical systems

AU - Ampilova, Natalia

AU - Soloviev, Igor

N1 - Conference code: 39

PY - 2019/6/1

Y1 - 2019/6/1

N2 - We consider a method of applied symbolic dynamics which may be used to obtain wide spectrum of characteristics of complex dynamical systems: approximation of invariant sets, estimation of topological entropy and approximation of invariant measures. The method has received wide acceptance in studying complex dynamical systems. The main idea of the method is to describe the system behaviour approximately by means of an oriented graph (called symbolic image). Such a graph is a representation of symbolic dynamical system which is more appropriately known as topological Markov chain. There exists a correspondence between trajectories of a given system and paths on the graph, which allows us to design algorithms for estimation of topological entropy, approximate invariant measures of a given system by using stationary flows on the graph and calculate corresponding metric entropies. These values characterize complex behaviour of dynamical systems such as the existence of trajectories with large periods and chaotic regimes. The results of experiments are given for systems with chaotic dynamics.

AB - We consider a method of applied symbolic dynamics which may be used to obtain wide spectrum of characteristics of complex dynamical systems: approximation of invariant sets, estimation of topological entropy and approximation of invariant measures. The method has received wide acceptance in studying complex dynamical systems. The main idea of the method is to describe the system behaviour approximately by means of an oriented graph (called symbolic image). Such a graph is a representation of symbolic dynamical system which is more appropriately known as topological Markov chain. There exists a correspondence between trajectories of a given system and paths on the graph, which allows us to design algorithms for estimation of topological entropy, approximate invariant measures of a given system by using stationary flows on the graph and calculate corresponding metric entropies. These values characterize complex behaviour of dynamical systems such as the existence of trajectories with large periods and chaotic regimes. The results of experiments are given for systems with chaotic dynamics.

KW - dynamical systems

KW - applied symbolic dynamics

KW - topological entropy

KW - symbolic image

KW - invariant measure

KW - Applied symbolic dynamics

KW - Invariant measure

KW - Topological entropy

KW - Symbolic image

KW - Dynamical systems

UR - http://www.scopus.com/inward/record.url?scp=85069481001&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/method-applied-symbolic-dynamics-investigation-dynamical-systems

U2 - 10.21595/vp.2019.20698

DO - 10.21595/vp.2019.20698

M3 - Conference contribution

VL - 25

T3 - Vibroengineering Procedia

SP - 128

EP - 134

BT - VP Vibroengineering Procedia

PB - JVE International Ltd.

CY - Kaunas, Lithuania

T2 - 39th International JVE Conference

Y2 - 25 June 2019 through 26 June 2019

ER -