Bifurcation of a disappearance of a non-compact heteroclinic curve

Olga V. Pochinka ^[2] ; Valeriya I. Shmukler ^[1] ; Elena A. Talanova ^[1]
1. [1] Higher School of Economics, National Research University
  
  Higher School of Economics, National Research University
  
  Rusia
2. [2] National Research University Higher School of Economics, Rusia; Nizhny Novgorod State University, Rusia
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 4, 2023
Idioma: inglés
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Resumen
- In the present paper, we describe a scenario of a disappearance of a non-compact heteroclinic curve for a three-dimensional diffeomorphism. As a consequence, it is established that 3-diffeomorphisms with a unique heteroclinic curve and fixed points of pairwise different Morse indices exist only on the 3-sphere. The described scenario is directly related to the reconnection processes in the solar corona, the mathematical essence of which, from the point of view of the magnetic charging topology, consists of a disappearance or a birth of non-compact heteroclinic curves.