Non-degenerate unfolding conjecture for homoclinic tangencies of Beltrami fields
Non-degenerate unfolding conjecture for homoclinic tangencies of Beltrami fields
Let be a Beltrami field, and let a periodic saddle orbit of have a homoclinic tangency. A homoclinic tangency is non-degenerately unfolded in when it admits a non-degenerate unfolding by a family of Beltrami fields in . Non-degenerate unfolding conjecture. Every homoclinic tangency for a periodic saddle orbit of a Beltrami field unfolds non-degenerately in . This is proposed as the Beltrami counterpart of the known result for smooth volume-preserving vector fields, and would clarify the generic dynamical behavior of Beltrami fields near homoclinic tangencies. The supplied text does not give a resolution.
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Primary source
Pierre Berger, Anna Florio and Daniel Peralta-Salas, “Steady Euler flows on R^3 with wild and universal dynamics”, arXiv:2202.02848 (2022).
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