Related papers: Dynamics inside Fatou sets in higher dimensions

In F-theory GUTs interactions between fields are typically localised at points of enhanced symmetry in the internal dimensions implying that the coefficient of the associated operator can be studied using a local wavefunctions overlap…

Let f_n be a sequence of analytic functions in a domain U with a common attracting fixed point z_0. Suppose that f_n converges to f_0 uniformly on each compact subset of U and that z_0 is a Siegel point of f_0. We establish a sufficient…

In the paper we describe basin of attraction of the $p$-adic dynamical system $f(x)=x^3+ax^2$. Moreover, we also describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the…

Let $(X,d)$ be a compact metric space, $f:X\rightarrow X$ be a continuous transformation with the specification property. we consider non-dense orbit set $E(z_0)$ and show that for any non-transitive point $z_0\in X$, this set $E(z_0)$ is…

The study of circular orbits in spacetime is of astrophysical importance. The identification and classification of circular orbits in both static and stationary spacetimes remains an active area of interest. Even in the simplest static…

We examine the quantum motion of two particles interacting through a contact force which are confined in a rectangular domain in two and three dimensions. When there is a difference in the mass scale of two particles, adiabatic separation…

Under a potential-theoretical hypothesis named $f$-Property with $f$ satisfying $\displaystyle\int_t^\infty \dfrac{da}{a f(a)}<\infty$, we show that the Kobayashi metric $K(z,X)$ on a weakly pseudoconvex domain $\Om$, satisfies the estimate…

Let $ E $ be a non-empty compact subset of the Riemann sphere and $T$ be a rational map of degree at least two. We study the associated \emph{orbital set}, that is, the backwards orbit of $E$ under $T$, and study the relationship between…

We show that the Feng-Xiong lower bound of $1/2$ for the box dimension of $\alpha\beta$-sets is tight. We also study how much of an $\alpha\beta$-orbit ``carries the dimension'': deleting an arbitararily small positive density set of times…

We show, both theoretically and experimentally, that the propagation of optical vortices in free space can be analysed by using the width ($w(z)$) of the host Gaussian beam and the inner and outer radii of the vortex beam at the source…

We study the relationship between pairs of topological dynamical systems $ (X,T) $ and $ (X',T') $, where $ (X',T') $ is the quotient of $ (X,T) $ under the action of a finite group $ G $. We describe three phenomena concerning the…

We study the behaviour of Yukawa and Newtonian gravitational forces in a cubic box with fully periodic boundaries commonly encountered in N-body simulations of the structure formation. Placing a single gravitating body at the origin of…

We consider the family of entire transcendental maps given by $F_{\lambda,m}= \lambda z^m exp(z)$ where m>=2. All functions $F_{\lambda,m}$ have a superattracting fixed point at z=0, and a critical point at z=-m. In the dynamical plane we…

We have investigated the accelerating behaviour of the universe in $f(Q,T)$ gravity in an isotropic and homogeneous space-time. We have initially derive the dynamical parameters in the general form of $f(Q,T)=\alpha Q^{m}+\beta T$ [Xu et…

The density stratification in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting features. In particular, numerical and lab experiments show that, in two…

We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models; depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first…

We experimentally study the behavior of a particle slightly denser than the surrounding liquid in solid body rotating flow. Earlier work revealed that a heavy particle has an unstable equilibrium point in unbounded rotation flows. In the…

A superposition of the Pauli and orbital coupling of a high magnetic field to charge carriers in a charge-density-wave (CDW) system is proposed to give rise to transitions between subphases with quantized values of the CDW wavevector. By…

Let $f(z,w)=(p(z),q(z,w))$ be a holomorphic skew product with a superattracting fixed point at the origin. In the previous paper we have succeeded to specify a dominant term of $q$ by the order of $p$ and the Newton polygon of $q$ and to…

Three dimensional H\'non-like map $$ F(x,y,z) = (f(x) - \epsilon (x,y,z),\ x,\ \delta (x,y,z)) $$ is defined on the cubic box $ B $. An invariant space under renormalization would appear only in higher dimension. Consider renormalizable…