Related papers: Parabolic Bifurcations in Complex Dimension 2

Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to…

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 study $C^r$ ($5 \le r \le \infty$) diffeomorphisms on closed manifolds of dimension at least three with a heteroclinic cycle between two hyperbolic periodic points. At each point, the unstable direction is one dimensional, and the stable…

We study diffeomorphisms $f$ with heterodimensional cycles, that is, heteroclinic cycles associated to saddles $p$ and $q$ with different indices. Such a cycle is called fragile if there is no diffeomorphism close to $f$ with a robust cycle…

In the physics literature, Bilal--Fock--Kogan \cite{BFK} introduced the idea of parabolic reduced flat connections on a surface to give a geometric origin to $W$-algebras. In this paper, we combine these ideas with higher complex…

We give a normal form for families of 3-dimensional Poisson structures. This allows us to classify singularities with nonzero 1-jet and typical bifurcations. The Appendix contains corollaries on classification of families of integrable…

An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…

We explore different families of quasi-periodically Forced Logistic Maps for the existence of universality and self-similarity properties. In the bifurcation diagram of the Logistic Map it is well known that there exist parameter values…

We study bifurcation mechanisms for the appearance of hyperchaotic attractors in three-dimensional diffeomorphisms, i.e., such attractors whose orbits have two positive Lyapunov exponents in numerical experiments. In order to possess this…

Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…

We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal $\alpha$-Family of Maps depending on a single parameter $\alpha > 0$ which is the order of the fractional derivative in the nonlinear…

We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results. This general approach does…

This work deals with bifurcation and the chaotic behavior in one dimensional chains of small particles. We consider two distinct possibilities, one where the particles are modeled by a fourth-order potential which was already studied. We…

Inspecting a $p$-dimensional parameter space by means of $(p-1)$-dimensional slices, changes can be detected that are only determined by the geometry of the manifolds that compose the bifurcation set. We refer to these changes as geometric…

We focus on the qualitative analysis of the phase portraits arising in the three-parameter FitzHugh-Nagumo system and its compactified form. The investigation is split into three parameter-dependent cases. In one of these cases, the system…

We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…

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…

We give a geometric description of the parabolic bifurcation locus in the space $\operatorname{Rat}_d$ of all rational functions on $\mathbb{P}^1$ of degree $d>1$, generalizing the study by Morton and Vivaldi in the case of monic…

We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The…

This paper studies the distribution of characteristic multipliers, the structure of submanifolds, the phase diagram, bifurcations and chaotic motions in the potential field of rotating highly irregular-shaped celestial bodies (hereafter…