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Comparatively simple models, with low energy structure similar to that of the MSSM, but with far fewer arbitrary parameters, can be constructed in which supersymmetry is dynamically broken at low energies. The phenomenology of these models…
Necessary conditions for asymptotic stability and stabilizability of subsets for dynamical and control systems are obtained. The main necessary condition is homotopical and is in turn used to obtain a homological one. A certain extension is…
The steady states of two vibrated granular gases separated by an adiabatic piston are investigated. The system exhibits a non-equilibrium phase transition with an spontaneous symmetry breaking. Even if the gases at both sides of the piston…
The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time…
Solutions of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent Riemannian metric.
According to quantum mechanics chiral molecules, that is molecules that rotate the polarization of light, should not exist. The simplest molecules which can be chiral have four or more atoms with two arrangements of minimal potential energy…
In this paper we provide a criterion for global secondary bifurcation via symmetry breaking. As an application, the occurrence of period-doubling bifurcations for the Lugiato-Lefever equation is proved.
For Hamiltonian systems with spherical symmetry there is a marked difference between zero and non-zero momentum values, and amongst all relative equilibria with zero momentum there is a marked difference between those of zero and those of…
Dynamical symmetry breaking provides a possible solution to the electroweak hierarchy problem. It requires new strong interactions that are effective at some high-energy scale. If there is no light Higgs boson, this scale is constrained to…
Monotone systems preserve a partial ordering of states along system trajectories and are often amenable to separable Lyapunov functions that are either the sum or the maximum of a collection of functions of a scalar argument. In this paper,…
Employing an arbitrary velocity gauge transformation this contribution argues that the breaking of time symmetry is a natural consequence of irreversibility.
The space of stability conditions on a triangulated category is naturally partitioned into subsets $U(A)$ of stability conditions with a given heart $A$. If $A$ has finite length and $n$ simple objects then $U(A)$ has a simple geometry,…
While there have been many studies examining the stability of hierarchical triple systems, the meaning of ``stability'' is somewhat vague and has been interpreted differently in previous literatures. The present paper focuses on ``Lagrange…
In this paper, the concepts and the direct theorems of stability in the sense of Liapunov, within the framework of Birkhoffian dynamical systems on manifolds, are considered. The Liapunov-type functions are constructed for linear and…
We consider a conservative system with small periodic perturbations under the assumption that the divergence of the perturbed system is negative. The main theorems provide universal sufficient conditions for the existence and asymptotic…
We obtain symmetry results for solutions of an elliptic system of equation possessing a cooperative structure. The domain in which the problem is set may possess "holes" or "small vacancies" (measured in terms of capacity) along which the…
In this talk I review modern theories of dynamical electroweak symmetry breaking and some of their signatures at Run II of the Tevatron collider.
A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random…
For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…
For systems evolving on a Riemannian manifold, we propose converse Lyapunov theorems for asymptotic and exponential stability. The novelty of the proposed approach is that is does not rely on local Euclidean coordinate, and is thus valid on…