Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps

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Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps. / Kryzhevich, Sergey ; Avrutin , Viktor ; Begun, Nikita ; Rachinskii , Dmitrii ; Tajbakhsh, Khosro .

In: Axioms, Vol. 10, No. 2, 80, 05.2021.

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

BibTeX

@article{1719c50e63114f60a98ce69d38b83ca3,

title = "Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps",

abstract = "We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.",

keywords = "interval translation maps, ergodic measures, symbolic model, robustness, risk management, Ergodic measures, Interval translation maps, Closing lemma, Robustness, Symbolic model, Risk management",

author = "Sergey Kryzhevich and Viktor Avrutin and Nikita Begun and Dmitrii Rachinskii and Khosro Tajbakhsh",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = may,

doi = "10.3390/axioms10020080",

language = "English",

volume = "10",

journal = "Axioms",

issn = "2075-1680",

publisher = "MDPI AG",

number = "2",

}

RIS

TY - JOUR

T1 - Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps

AU - Kryzhevich, Sergey

AU - Avrutin , Viktor

AU - Begun, Nikita

AU - Rachinskii , Dmitrii

AU - Tajbakhsh, Khosro

PY - 2021/5

Y1 - 2021/5

N2 - We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.

AB - We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.

KW - interval translation maps

KW - ergodic measures

KW - symbolic model

KW - robustness

KW - risk management

KW - Ergodic measures

KW - Interval translation maps

KW - Closing lemma

KW - Robustness

KW - Symbolic model

KW - Risk management

UR - https://www.mdpi.com/2075-1680/10/2/80

UR - http://www.scopus.com/inward/record.url?scp=85106901979&partnerID=8YFLogxK

U2 - 10.3390/axioms10020080

DO - 10.3390/axioms10020080

M3 - Article

VL - 10

JO - Axioms

JF - Axioms

SN - 2075-1680

IS - 2

M1 - 80

ER -

ID: 76470083