Related papers: On trigonometric skew-products over irrational cir…
We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift $\binom{j}{2} \omega+jy+x \mod 1$ for irrational $\omega$. We prove that the eigenvalue distribution of…
An existence result is shown for the asymptotic Dirichlet problem for harmonic maps from the product of the hyperbolic planes to the hyperbolic space, where the Dirichlet data is given on the distinguished boundary (the product of the…
Let $R$ be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an $R$-algebra with involution, which are rationally ismorphic and have isomorphic semisimple coradicals,…
We provide an equivalent characterisation for the existence of one-dimensional irrational rotation factors of conservative torus homeomorphisms that are not eventually annular. It states that an area-preserving non-annular torus…
We prove that for continuous maps on the interval, the existence of an n-cycle, implies the existence of n-1 points which interwind the original ones and are permuted by the map. We then use this combinatorial result to show that piecewise…
It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the…
We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…
In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation.…
We prove the rigidity and vanishing of several indices of "geometrically natural" twisted Dirac operators on almost even-Clifford Hermitian manifolds admitting circle actions by automorphisms.
We use Clifford's geometric algebra to extend the Stuart-Landau system to dimensions $D >2$ and give an exact solution of the oscillator equations in the general case. At the supercritical Hopf bifurcation marked by a transition from stable…
In reversible dynamical systems, it is frequently of importance to understand symmetric features. The aim of this paper is to explore symmetric periodic points of reversible maps on planar domains invariant under a reflection. We extend…
The orbital basis is natural when one needs to calculate the effect of local interactions or to unravel the role of orbital physics in the response to external probes. In systems with nonsymmorphic point groups, such as the iron-based…
We prove that there is a residual set of families of smooth or analytic unimodal maps with quadratic critical point and negative Schwarzian derivative such that almost every non-regular parameter is Collet-Eckmann with subexponential…
For the PT symmetric potential of Dorey, Dunning and Tateo we show that in the large angular momentum (i.e., strongly spiked) limit the low-lying eigenstates of this popular non-Hermitian problem coincide with the shifted Hermitian harmonic…
This paper concerns the existence of multiple rotating quasi-periodic solutions for second order Hamiltonian systems with sub-quadratic potential. Such solutions have the form $x(t+T)=Qx(t)$ for some orthogonal matrix $Q$. To deal with such…
We study the stroboscopic dynamics of a spin-$S$ object subjected to $\delta$-function kicking in the transverse magnetic field which is generated following the Fibonacci sequence. The corresponding classical Hamiltonian map is constructed…
We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…
We define renormalised energies for maps that describe the first-order asymptotics of harmonic maps outside of singularities arising due to obstructions generated by the boundary data and the mutliple connectedness of the target manifold.…
The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…
We prove that quasi-isometries of horospherical products of hyperbolic spaces are geometrically rigid in the sense that they are uniformly close to product maps, this is a generalisation of the result obtained by Eskin, Fisher and Whyte in…