Related papers: Universal Scaling in Saddle-Node Bifurcation Casca…
Universal scaling of entanglement estimators of critical quantum systems has drawn a lot of attention in the past. Recent studies indicate that similar universal properties can be found for bipartite information estimators of classical…
The three-rotor system concerns equally massive point particles moving on a circle subject to attractive cosine potentials of strength $g$. The quantum theory models chains of coupled Josephson junctions. Classically, it displays…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…
We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical…
The accumulation point of the period-tripling bifurcation cascade in complex quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv. 38:1, 1983, 187), and independently by Cvitanovic and Myrheim (Phys.Lett. A94:8, 1983,…
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.
Scaling theory predicts complete localization in $d=2$ in quantum systems belonging to orthogonal class (i.e. with time-reversal symmetry and spin-rotation symmetry). The conductance $g$ behaves as $g \sim exp(-L/l)$ with system size $L$…
It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal correspondence of their quantum spectral statistics with random matrix models. We argue…
Motivated by a possibility to optimize modelling of the population evolution we postulate a generalization of the well-know logistic map. Generalized difference equation reads: \begin{equation} x_{n+1}=rx^p_n(1-x^q_n), \end{equation}…
We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible maps unfolding generally the…
These lecture notes have been written for a short introductory course on universality and renormalization group techniques given at the VIII Modave School in Mathematical Physics by the author, intended for PhD students and researchers new…
By appropriate scaling of coupling constants a one-parameter family of ensembles of two-dimensional geometries is obtained, which interpolates between the ensembles of (generalized) causal dynamical triangulations and ordinary dynamical…
The evergreen problem of a bead on a rotating hoop shows a multitude of bifurcations when the bead moves with friction. This motion is studied for different values of the damping coefficient and rotational speeds of the hoop. Phase…
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo…
By means of a linear scaling of the variables we convert a singular bifurcation equation in $\R^n$ into an equivalent equation to which the classical implicit function theorem can be directly applied. This allows to deduce the existence of…
When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom a saddle point appears, which is called the Stark saddle point. For energies slightly above the saddle point energy one can find classical…
The lowest order resonant bifurcations of a periodic orbit of a Hamiltonian system with two degrees of freedom have frequency ratio 1:1 (saddle-centre) and 1:2 (period-doubling). The twist, which is the derivative of the rotation number…
We study bifurcation for the constant scalar curvature equation along a one-parameter family of Riemannian metrics on the total space of a harmonic Riemannian submersion. We provide an existence theorem for bifurcation points and a…
We consider discrete nonlinear Schr\"odinger equations of n sites with periodic boundary conditions. These equations have n branches of standing waves that bifurcate from zero. Traveling waves appear as a symmetry-breaking from the standing…
The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally…