Opis

• Tytuł:
  Multiple connecting geodesics of a Randers-Kropina metric via homotopy theory for solutions of an affine control system
• Twórca:
  Caponio, Erasmo;
  Javaloyes, Miguel Angel;
  Masiello, Antonio
• Opis:
  We consider a geodesic problem in a manifold endowed with a Randers-Kropina metric. This is a type of a singular Finsler metric arising both in the description of the lightlike vectors of a spacetime endowed with a causal Killing vector field and in the Zermelo's navigation problem with a wind represented by a vector field having norm not greater than one. By using Lusternik-Schnirelman theory, we prove existence of infinitely many geodesics between two given points when the manifold is not contractible. Due to the type of non-holonomic constraints that the velocity vectors must satisfy, this is achieved thanks to some recent results about the homotopy type of the set of solutions of an affine control system associated with a totally non-integrable distribution.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Erasmo Caponio, Miguel Angel Javaloyes, Antonio Masiello
• Data:
  2023.02.26
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 61, No 1 (March 2023); 527 - 547;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/42826/34994 ;https://apcz.umk.pl/TMNA/article/view/42826/34995
• Temat i słowa kluczowe:
  Randers metric;
  Kropina metric;
  geodesics;
  affine control systems;
  causal Killing field;
  Zermelo's navigation problem;
  Primary: 58E10, 53C22, 53C60;
  Secondary: 34H05
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/42826
• Dostawca danych:
  Akademicka Platforma Czasopism
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