Existence of small loops in a bifurcation diagram near degenerate eigenvalues

Taoufik Hmidi, Coralie Renault

Research output: Contribution to journalArticlepeer-review


In this paper, we study the global structure of a bifurcation diagram for rotating doubly connected patches near a degenerate case for incompressible Euler equations. We show that branches with the same symmetry merge, forming a small loop, provided that they are close enough. This gives an analytical proof for the numerical observations conducted in the recent work by de la Hoz et al (2016 SIAM J. Math. Anal. 48 1892-928).

Original languageEnglish (US)
Pages (from-to)3821-3852
Number of pages32
Issue number10
StatePublished - Sep 15 2017


  • Euler equations
  • bifurcation diagram
  • relative equilibria

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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