Development of concept of topological entropy for systems with multiple time

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Development of concept of topological entropy for systems with multiple time. / Anikushin, M. M.; Reitmann, V.

In: Differential Equations, Vol. 52, No. 13, 01.12.2016, p. 1655-1670.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{4b0d7766541a4b3d807289b42a8f3ec8,

title = "Development of concept of topological entropy for systems with multiple time",

abstract = "We study the topological entropy for dynamical systems with discrete or continuous multiple time. Due to the generalization of a well-known one time-dimensional result we show that the definition of topological entropy, using the approach for subshifts, leads to the zero entropy for many systems different from subshift. We define a new type of relative topological entropy to avoid this phenomenon. The generalization of Bowen{\textquoteright}s power rule allows us to define topological and relative topological entropies for systems with continuous multiple time. As an application, we find a relation between the relative topological entropy and controllability of linear systems with continuous multiple time.",

author = "Anikushin, {M. M.} and V. Reitmann",

year = "2016",

month = dec,

day = "1",

doi = "10.1134/S0012266116130012",

language = "English",

volume = "52",

pages = "1655--1670",

journal = "Differential Equations",

issn = "0012-2661",

publisher = "Pleiades Publishing",

number = "13",

}

RIS

TY - JOUR

T1 - Development of concept of topological entropy for systems with multiple time

AU - Anikushin, M. M.

AU - Reitmann, V.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - We study the topological entropy for dynamical systems with discrete or continuous multiple time. Due to the generalization of a well-known one time-dimensional result we show that the definition of topological entropy, using the approach for subshifts, leads to the zero entropy for many systems different from subshift. We define a new type of relative topological entropy to avoid this phenomenon. The generalization of Bowen’s power rule allows us to define topological and relative topological entropies for systems with continuous multiple time. As an application, we find a relation between the relative topological entropy and controllability of linear systems with continuous multiple time.

AB - We study the topological entropy for dynamical systems with discrete or continuous multiple time. Due to the generalization of a well-known one time-dimensional result we show that the definition of topological entropy, using the approach for subshifts, leads to the zero entropy for many systems different from subshift. We define a new type of relative topological entropy to avoid this phenomenon. The generalization of Bowen’s power rule allows us to define topological and relative topological entropies for systems with continuous multiple time. As an application, we find a relation between the relative topological entropy and controllability of linear systems with continuous multiple time.

UR - http://www.scopus.com/inward/record.url?scp=85014561836&partnerID=8YFLogxK

U2 - 10.1134/S0012266116130012

DO - 10.1134/S0012266116130012

M3 - Article

AN - SCOPUS:85014561836

VL - 52

SP - 1655

EP - 1670

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 13

ER -

ID: 73406138