Double Hopf bifurcation with strong resonances in delayed systems with nonlinearities.
The object of the present paper is to give a qualitative description of the bifurcation mechanisms associated with a closed invariant curve in three-dimensional maps, leading to its doubling, not related to a standard doubling of tori. We propose an explanation on how a closed invariant attracting curve, born via Neimark-Sacker bifurcation, can be transformed into a repelling one giving birth to a new attracting closed invariant curve which has doubled...
In this paper we construct on truncated current Lie algebras integrable hierarchies of partial differential equations, which generalize the Drinfeld-Sokolov hierarchies defined on Kac-Moody Lie algebras.
One gives the links between the notions of singular foliations, Γ-structures and momentum mapping in the context of symplectic geometry.
Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).
For n ≥ 2, the family of rational maps contains a countably infinite set of parameter values for which all critical orbits eventually land after some number κ of iterations on the point at infinity. The Julia sets of such maps are Sierpiński curves if κ ≥ 3. We show that two such maps are topologically conjugate on their Julia sets if and only if they are Möbius or anti-Möbius conjugate, and we give a precise count of the number of topological conjugacy classes as a function of n and κ.