Context. The MHD instabilities can generate complex field topologies even if the initial field configuration is a very simple one. Aims. We consider the stability properties of magnetic configurations containing a toroidal and an axial field. In this paper, we concentrate mainly on the behavior of non-axisymmetric perturbations in axisymmetric magnetic configurations. Methods. The stability is ...

We derive the non-perturbative corrections to the free energy of the two-matrix model in terms of its algebraic curve. The eigenvalue instantons are associated with the vanishing cycles of the curve. For the (p, q) critical points our results agree with the geometrical interpretation of the instanton effects recently discovered in the CFT approach. The form of the instanton corrections implies ...

We establish basic local existence as well as a stability result concerning small perturbations of the Catenoid minimal surface in R3 under hyperbolic vanishing mean curvature flow.

The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard...

We highlight a viable mechanism leading to the formation of dark energy structures on sub-horizon cosmological scales, starting from linear perturbations in scalar-tensor cosmologies. We show that the coupling of the dark energy scalar field, or Quintessence, to the Ricci scalar induces a “dragging” of its density perturbations through the general relativistic gravitational potentials. We discu...

This is the second in a series of works devoted to small non-selfadjoint perturbations of selfadjoint semiclassical pseudodifferential operators in dimension 2. As in our previous work, we consider the case when the classical flow of the unperturbed part is periodic. Under the assumption that the flow average of the leading perturbation vanishes identically, we show how to obtain a complete asy...

Minimally modified gravity is a class of models with only the two tensor degrees freedom as in general relativity. Using framework auxiliary constraints these can maintain dynamical cosmological background. The form thereby restricted by requirement dark energy and avoidance breakdown perturbation theory. Studying linear perturbations around FLRW background results are, however, quite insensiti...

In the present paper, we study several qualitative properties of a class of nonlinear switched systems under certain switching laws. First, we show that if all the subsystems are linear time-invariant and the system matrices are commutative componentwise and stable, then the entire switched system is globally exponentially stable under arbitrary switching laws. Next, we study the above linear s...