Related papers: Unstable higher Toda brackets III
Using the irreducibility of a natural irreducible representation of the theta group of an ample line bundle on an abelian variety, we derive a bound for the number of $n$-torsion points that lie on a given theta divisor. We present also two…
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…
Unstable particles are notorious in perturbative quantum field theory for producing singular propagators in scattering amplitudes that require regularization by the finite width. In this review I discuss the construction of an effective…
In this letter we introduce the concept of stabilized vector solitons as nonlinear waves constructed by addition of mutually incoherent Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We…
A new and natural description of the category of unstable modules over the Steenrod algebra as a category of comodules over a bialgebra is given; the theory extends and unifies the work of Carlsson, Kuhn, Lannes, Miller, Schwartz, Zarati…
We present a systematic derivation for a general formula for the n-point coupling constant valid for affine Toda theories related to any simple Lie algebra {\bf g}. All n-point couplings with $n \geq 4$ are completely determined in terms of…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
We study the relation between perverse stability conditions and geometric stability conditions under blow up. We confirm a conjecture of Toda in some special cases and show that geometric stability conditions can be induced from perverse…
We prove stability bounds for Stokes-like virtual element spaces in two and three dimensions. Such bounds are also instrumental in deriving optimal interpolation estimates. Furthermore, we develop some numerical tests in order to…
In six- and seven-dimensional gauged supergravity, each scalar potential has one supersymmetric and one non-supersymmetric fixed points. The non-supersymmetric $AdS_7$ fixed point is perturbatively unstable. On the other hand, the…
We provide a new approach to stable ergodicity of systems with dominated splittings, based on a geometrical analysis of global stable and unstable manifolds of hyperbolic points. Our method suggests that the lack of uniform size of Pesin's…
We classify the non-supersymmetric, and perturbatively stable within $D=4$, AdS vacua of maximal $D=4$ supergravity with a dyonic ISO(7) gauging in a large sector of the supergravity. Seven such vacua are established within this sector, all…
A Toda equation is specified by a choice of a Lie group and a $\mathbb Z$-gradation of its Lie algebra. The Toda equations associated with loop groups of complex classical Lie groups, whose Lie algebras are endowed with integrable $\mathbb…
We give a birational description of the reduced schemes underlying the irreducible components of the nilpotent cone and the $\CC^\times$-fixed point locus of length two in the moduli space of Higgs bundles. Using these results, we prove…
We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of…
A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with…
We study the leading (LO) and the next-to-leading order (NLO) stability of multipole perturbations for a static dielectric M2-brane with spherical topology in the 11-dimensional maximally supersymmetric plane-wave background. We observe a…
We consider soliton dynamics and stability in a nonlinear lattice formed by alternating domains with focusing cubic and saturable nonlinearities. We find that in such lattices solitons centered on cubic domains may be stabilized even in…
We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive…
A detailed numerical stability analysis of the static, spherically symmetric globally regular solutions of the Einstein-Yang-Mills equations with a positive cosmological constant, Lambda, is carried out. It is found that the number of…