A new universal empirical function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes of dissipation: (i) strong dissipation and (ii) weak dissipation. For case (i) the model exhibits a route to chaos known as period doubling and the Feigenbaum constant along the bifurcations is obtained. When weak dissipation is considered the average action as well as its standard deviation are described using scaling arguments with critical exponents. The universal empirical function describes remarkably well a phase transition from limited to unlimited growth of the average action.
COBISS.SI-ID: 70483201
We present a simple WKB-like approach to obtain approximate analytic solutions to a certain class of time-dependent nonlinear 1D Hamiltonian oscillators. The case of homogeneous power-law potentials is solved explicitly in a closed form in the leading order. The accuracy of the approximation is surprisingly good and we illustrate it in the case of the quartic oscillator. PACS numbers: 02.30.Mv, 05.45.-a, 45.05.+x
COBISS.SI-ID: 68382465
We study the moduli-dependent prefactor of M5-instanton corrections to the superpotential in four-dimensional F-theory compactifications. In light of the M-theory and type IIb limits and also heterotic duality, we propose that the explicit moduli dependence of the prefactor can be computed by a study of zero modes localized at intersections between the instanton and seven-branes. We present an instanton prefactor in an E6 F-theory GUT which does not admit a heterotic dual and show that it vanishes if and only if a point of E8 enhancement is present in the instanton world volume. More generically, we discuss the relationship between points of E8 and superpotential zeroes and give sufficient conditions for such a point to cause a zero, even for an SU(5)GUT. We scan a large class of compactifications for instanton physics and demonstrate that many instantons have the same prefactor structure. We discuss the associated implications and complications for moduli stabilization. We present an explicit resolution and construction of G-flux in a generic E6 GUT and identify a global compactification of the local model spectral cover which happens to facilitate prefactor computations. Via a Leray spectral sequence, we demonstrate the relationship between right-movers of heterotic worldsheet instantons, 3-3 strings of euclidean D3 instantons, and the Fermi zero modes of M5-instantons.
COBISS.SI-ID: 73422593
We study analytic properties of the Poincaré return map and generalized focal values of analytic planar systems with a nilpotent focus or center. We use the focal values and the map to study the number of limit cycles of this kind of systems and obtain some new results on the lower and upper bounds of the maximal number of limit cycles bifurcating from the nilpotent focus or center. The main results generalize the classical Hopf bifurcation theory and establish the new bifurcation theory for the nilpotent case.
COBISS.SI-ID: 19592968
We propose a generalization of the notion of isochronicity for real polynomial autonomous systems to the case of complex two dimensional systems of ODEs. We study the generalized problem in the case of a quadratic system and a system with homogeneous cubic nonlinearities. Main tools of the study are algorithms of computational algebra based on the Groebner basis theory.
COBISS.SI-ID: 19324168