Existence of quasipatterns in the superposition of two hexagonal patterns
Résumé
Let us consider a quasilattice, spanned by the superposition of two hexagonal lattices in the plane, differing by a rotation of angle α. We study bifurcating quasipatterns solutions of the Swift-Hohenberg PDE, built on such a quasilattice, invariant under rotations of angle π/3. For nearly all α, we prove that in addition to the classical hexagonal patterns, there exist two branches of bifurcating quasipatterns, with equal amplitudes on each basic lattice.
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