Existence of quasipatterns in the superposition of two hexagonal patterns

Gérard Iooss (1, 2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 IUF - Institut universitaire de France

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.

Mots clés: pattern formation; small divisors; bifurcations; partial differential equations

Domaines: Equations aux dérivées partielles [math.AP]; Formation de Structures et Solitons [nlin.PS]; Systèmes dynamiques [math.DS]

Gérard Iooss. Existence of quasipatterns in the superposition of two hexagonal patterns. Nonlinearity, 2018, 32(9), pp.3163-3187. ⟨10.1088/1361-6544/ab230a⟩. ⟨hal-01891631⟩