The Structure of Global Attractors for Non-autonomous Perturbations of Gradient-Like Dynamical Systems

Cheban David

Conţinutul numărului revistei

Articolul precedent

Articolul urmator

351

SM ISO690:2012

CHEBAN, David. The Structure of Global Attractors for Non-autonomous Perturbations of Gradient-Like Dynamical Systems. In: Journal of Dynamics and Differential Equations, 2020, nr. 3(32), pp. 1113-1138. ISSN 1040-7294. DOI: https://doi.org/10.1007/s10884-019-09776-9

EXPORT metadate:
Google Scholar
Crossref
CERIF

DataCite
Dublin Core

Journal of Dynamics and Differential Equations

Numărul 3(32) / 2020 / ISSN 1040-7294

The Structure of Global Attractors for Non-autonomous Perturbations of Gradient-Like Dynamical Systems

DOI:https://doi.org/10.1007/s10884-019-09776-9

Pag. 1113-1138

Cheban David

Moldova State University

Disponibil în IBN: 6 octombrie 2020

Rezumat

In this paper we give the complete description of the structure of compact global (forward) attractors for non-autonomous perturbations of autonomous gradient-like dynamical systems under the assumption that the original autonomous system has a finite number of hyperbolic stationary solutions. We prove that the perturbed non-autonomous (in particular τ-periodic, quasi-periodic, Bohr almost periodic, almost automorphic, recurrent in the sense of Birkhoff) system has exactly the same number of invariant sections (in particular the perturbed systems has the same number of τ-periodic, quasi-periodic, Bohr almost periodic, almost automorphic, recurrent in the sense of Birkhoff solutions). It is shown the compact global (forward) attractor of non-autonomous perturbed system coincides with the union of unstable manifolds of this finite number of invariant sections.

Cuvinte-cheie
almost automorphic solutions, Almost periodic, chain-recurrent motions, global attractor, Gradient-like dynamical systems, non-autonomous perturbations

Cerif XML Export

<?xml version='1.0' encoding='utf-8'?>
<CERIF xmlns='urn:xmlns:org:eurocris:cerif-1.5-1' xsi:schemaLocation='urn:xmlns:org:eurocris:cerif-1.5-1 http://www.eurocris.org/Uploads/Web%20pages/CERIF-1.5/CERIF_1.5_1.xsd' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' release='1.5' date='2012-10-07' sourceDatabase='Output Profile'>
<cfResPubl>
<cfResPublId>ibn-ResPubl-111281</cfResPublId>
<cfResPublDate>2020-09-01</cfResPublDate>
<cfVol>32</cfVol>
<cfIssue>3</cfIssue>
<cfStartPage>1113</cfStartPage>
<cfISSN>1040-7294</cfISSN>
<cfURI>https://ibn.idsi.md/ro/vizualizare_articol/111281</cfURI>
<cfTitle cfLangCode='EN' cfTrans='o'>The Structure of Global Attractors for Non-autonomous Perturbations of Gradient-Like Dynamical Systems</cfTitle>
<cfKeyw cfLangCode='EN' cfTrans='o'>almost automorphic solutions; Almost periodic; chain-recurrent motions; global attractor; Gradient-like dynamical systems; non-autonomous perturbations</cfKeyw>
<cfAbstr cfLangCode='EN' cfTrans='o'><p>In this paper we give the complete description of the structure of compact global (forward) attractors for non-autonomous perturbations of autonomous gradient-like dynamical systems under the assumption that the original autonomous system has a finite number of hyperbolic stationary solutions. We prove that the perturbed non-autonomous (in particular &tau;-periodic, quasi-periodic, Bohr almost periodic, almost automorphic, recurrent in the sense of Birkhoff) system has exactly the same number of invariant sections (in particular the perturbed systems has the same number of &tau;-periodic, quasi-periodic, Bohr almost periodic, almost automorphic, recurrent in the sense of Birkhoff solutions). It is shown the compact global (forward) attractor of non-autonomous perturbed system coincides with the union of unstable manifolds of this finite number of invariant sections.</p></cfAbstr>
<cfResPubl_Class>
<cfClassId>eda2d9e9-34c5-11e1-b86c-0800200c9a66</cfClassId>
<cfClassSchemeId>759af938-34ae-11e1-b86c-0800200c9a66</cfClassSchemeId>
<cfStartDate>2020-09-01T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfResPubl_Class>
<cfClassId>e601872f-4b7e-4d88-929f-7df027b226c9</cfClassId>
<cfClassSchemeId>40e90e2f-446d-460a-98e5-5dce57550c48</cfClassSchemeId>
<cfStartDate>2020-09-01T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfPers_ResPubl>
<cfPersId>ibn-person-645</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2020-09-01T24:00:00</cfStartDate>
</cfPers_ResPubl>
<cfFedId>
<cfFedIdId>ibn-doi-111281</cfFedIdId>
<cfFedId>10.1007/s10884-019-09776-9</cfFedId>
<cfStartDate>2020-09-01T24:00:00</cfStartDate>
<cfFedId_Class>
<cfClassId>31d222b4-11e0-434b-b5ae-088119c51189</cfClassId>
<cfClassSchemeId>bccb3266-689d-4740-a039-c96594b4d916</cfClassSchemeId>
</cfFedId_Class>
<cfFedId_Srv>
<cfSrvId>5123451</cfSrvId>
<cfClassId>eda2b2e2-34c5-11e1-b86c-0800200c9a66</cfClassId>
<cfClassSchemeId>5a270628-f593-4ff4-a44a-95660c76e182</cfClassSchemeId>
</cfFedId_Srv>
</cfFedId>
</cfResPubl>
<cfPers>
<cfPersId>ibn-Pers-645</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-645-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2020-09-01T24:00:00</cfStartDate>
<cfFamilyNames>Cheban</cfFamilyNames>
<cfFirstNames>David</cfFirstNames>
</cfPersName_Pers>
</cfPers>
<cfSrv>
<cfSrvId>5123451</cfSrvId>
<cfName cfLangCode='en' cfTrans='o'>CrossRef DOI prefix service</cfName>
<cfDescr cfLangCode='en' cfTrans='o'>The service of issuing DOI prefixes to publishers</cfDescr>
<cfKeyw cfLangCode='en' cfTrans='o'>persistent identifier; Digital Object Identifier</cfKeyw>
</cfSrv>
</CERIF>