<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-05416254</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-04T08:50:25+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Dynamical systems on torus related to general Heun equations: phase-lock areas and constriction breaking</title>
            <author role="aut">
              <persName>
                <forename type="first">Artem</forename>
                <surname>Alexandrov</surname>
              </persName>
              <idno type="halauthorid">3523750-0</idno>
              <affiliation ref="#struct-7074"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Alexey</forename>
                <surname>Glutsyuk</surname>
              </persName>
              <email type="md5">e7c9197b524bc962f0c6daa8f352a0df</email>
              <email type="domain">ens-lyon.fr</email>
              <idno type="idhal" notation="string">aglutsyu</idno>
              <idno type="idhal" notation="numeric">10670</idno>
              <idno type="halauthorid" notation="string">18260-10670</idno>
              <idno type="IDREF">https://www.idref.fr/169156044</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-6432-2725</idno>
              <affiliation ref="#struct-106"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Alexey</forename>
                <surname>Glutsyuk</surname>
              </persName>
              <email type="md5">e7c9197b524bc962f0c6daa8f352a0df</email>
              <email type="domain">ens-lyon.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-12-15 10:44:22</date>
              <date type="whenModified">2025-12-17 03:14:28</date>
              <date type="whenReleased">2025-12-16 11:48:58</date>
              <date type="whenProduced">2025-12-15</date>
              <date type="whenEndEmbargoed">2025-12-15</date>
              <ref type="file" target="https://hal.science/hal-05416254v1/document">
                <date notBefore="2025-12-15"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-05416254v1/file/General_Heun_Phase_Lock_JoDE.pdf" id="file-5416254-4635280">
                <date notBefore="2025-12-15"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2507.07282"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="111341">
                <persName>
                  <forename>Alexey</forename>
                  <surname>Glutsyuk</surname>
                </persName>
                <email type="md5">e7c9197b524bc962f0c6daa8f352a0df</email>
                <email type="domain">ens-lyon.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-05416254</idno>
            <idno type="halUri">https://hal.science/hal-05416254</idno>
            <idno type="halBibtex">alexandrov:hal-05416254</idno>
            <idno type="halRefHtml">2025</idno>
            <idno type="halRef">2025</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-5416254-4635280"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENS-LYON">École Normale Supérieure de Lyon</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="UDL">UDL</idno>
            <idno type="stamp" n="UNIV-LYON">Université de Lyon</idno>
          </seriesStmt>
          <notesStmt/>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Dynamical systems on torus related to general Heun equations: phase-lock areas and constriction breaking</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Artem</forename>
                    <surname>Alexandrov</surname>
                  </persName>
                  <idno type="halauthorid">3523750-0</idno>
                  <affiliation ref="#struct-7074"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Alexey</forename>
                    <surname>Glutsyuk</surname>
                  </persName>
                  <email type="md5">e7c9197b524bc962f0c6daa8f352a0df</email>
                  <email type="domain">ens-lyon.fr</email>
                  <idno type="idhal" notation="string">aglutsyu</idno>
                  <idno type="idhal" notation="numeric">10670</idno>
                  <idno type="halauthorid" notation="string">18260-10670</idno>
                  <idno type="IDREF">https://www.idref.fr/169156044</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-6432-2725</idno>
                  <affiliation ref="#struct-106"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">2507.07282</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Heun equation</term>
                <term xml:lang="en">phase-locking</term>
                <term xml:lang="en">rotation number quantization</term>
              </keywords>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>The overdamped Josephson junction in superconductivity theory can be modeled by the family of dynamical systems on the torus, which is known as the RSJ model. This family admits an equivalent description by a family of second-order differential equations: special double confluent Heun equations. In the present paper, we construct two new families of dynamical systems on torus that can be equivalently described by a family of general Heun equations (GHE), with four singular points, and confluent Heun equations, with three singular points. The first family, related to GHE, is a deformation of the RSJ model, which will be denoted by dRSJ. The phase-lock areas of a family of dynamical systems on the torus are those level subsets of the rotation number function that have nonempty interiors. It is known that for the RSJ model, the rotation number quantization effect occurs: phase-lock areas exist only for integer rotation number values. Moreover, each phase-lock area is a chain of domains separated by points. Those separation points that do not lie on the abscissa axis are called constrictions. In the present paper, we study phase-lock areas in the new family dRSJ. The quantization effect remains valid in this family. On the other hand, we show that in the new family dRSJ the constrictions break down.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-7074" status="VALID">
          <orgName>Institute for Information Transmission Problems</orgName>
          <desc>
            <address>
              <country key="RU"/>
            </address>
            <ref type="url">http://www.ippi.ru/en/structure</ref>
          </desc>
          <listRelation>
            <relation active="#struct-217892" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-106" status="VALID">
          <idno type="IdRef">192542389</idno>
          <idno type="ISNI">000000040384775X</idno>
          <idno type="RNSR">199812077R</idno>
          <idno type="ROR">https://ror.org/05n21n105</idno>
          <idno type="Wikidata">Q30262468</idno>
          <orgName>Unité de Mathématiques Pures et Appliquées</orgName>
          <orgName type="acronym">UMPA-ENSL</orgName>
          <date type="start">1999-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.umpa.ens-lyon.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-6818" type="direct"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation name="UMR5669" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-217892" status="VALID">
          <idno type="ROR">https://ror.org/05qrfxd25</idno>
          <orgName>Russian Academy of Sciences [Moscow]</orgName>
          <orgName type="acronym">RAS</orgName>
          <desc>
            <address>
              <addrLine>Leninsky Ave, 14, Moscow, Russie, 119991</addrLine>
              <country key="RU"/>
            </address>
            <ref type="url">http://www.ras.ru/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-6818" status="VALID">
          <idno type="IdRef">149154992</idno>
          <idno type="ISNI">0000000123319856</idno>
          <idno type="ROR">https://ror.org/04zmssz18</idno>
          <idno type="Wikidata">Q10159</idno>
          <orgName>École normale supérieure de Lyon</orgName>
          <orgName type="acronym">ENS de Lyon</orgName>
          <date type="start">2010-01-01</date>
          <desc>
            <address>
              <addrLine>15 parvis René Descartes - BP 7000 - 69342 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ens-lyon.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301088" status="VALID">
          <idno type="ROR">https://ror.org/01rk35k63</idno>
          <orgName>Université de Lyon</orgName>
          <desc>
            <address>
              <addrLine>92 rue Pasteur - CS 30122, 69361 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-lyon.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>