Related papers: Supercritical equivariant biharmonic maps from $\m…

We present statistical biharmonic maps, a new class of mappings between statistical manifolds naturally derived from a variation problem. We give the Euler-Lagrange equation of this problem and prove that improper affine hyperspheres induce…

The multicritical point at which both a 3-component and a 2-component order parameters order simultaneously in 3 dimensions is shown to have the critical behavior of the decoupled fixed point, with separate n=3 and n=2 behavior. This…

In this paper, we explore supersymmetric and 2d analogs of the SYK model. We begin by working out a basis of (super)conformal eigenfunctions appropriate for expanding a four-point function. We use this to clarify some details of the 1d…

We consider a class of doubly intermittent maps with critical points, unbounded derivative and regularly varying tails. Under some mild assumptions we prove the existence of a unique mixing absolutely continuous invariant measure and give…

We report on transcritical bifurcations of periodic orbits in non-integrable two-dimensional Hamiltonian systems. We discuss their existence criteria and some of their properties using a recent mathematical description of transcritical…

We consider a (mathbb{Z}_2)-equivariant flow in (mathbb{R}^{4}) with an integral of motion and a hyperbolic equilibrium with a transverse homoclinic orbit (Gamma). We provide criteria for the existence of stable and unstable invariant…

We construct explicit examples of Dirac-harmonic maps $(\phi, \psi)$ between Riemannian manifolds $(M,g)$ and $(N,g')$ which are non-trivial in the sense that $\phi$ is not harmonic. When $\dim M=2$, we also produce examples where $\phi$ is…

We show that any dynamics on any planar set $S$ discrete in some domain $D$ can be realized by the postcritical dynamics of a function holomorphic in $D$, up to a small perturbation. A key step in the proof, and a result of independent…

We study the dynamics of a piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in $\mathbb{R}^2$. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each…

A group-theoretical approach to the construction of quasiperiodic tilings of a Euclidean plane, possessing five-fold symmetry, is applied. Of the infinitely many of variants of quasiperiodic partitions of the plane, possessing the dihedral…

We study biharmonic maps between conformally compact manifolds, a large class of complete manifolds with bounded geometry, asymptotically negative curvature, and smooth compactification. These metrics provide a far-reaching generalization…

We study compactness and noncompactness phenomena for the CR Yamabe equation on compact strictly pseudoconvex CR manifolds. First, in dimension five we establish uniform \emph{a priori} estimates for families of positive solutions of…

We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings…

We give a hierarchy of many-parameter families of maps of the interval [0,1] with an invariant measure and using the measure, we calculate Kolmogorov--Sinai entropy of these maps analytically. In contrary to the usual one-dimensional maps…

We study the boundary limit of the bulk isometries of AdS x S. The superconformal symmetry is realized on the coordinates of the AdS boundary, the fermionic superspace coordinates, and the harmonics on the sphere. We show how these may be…

Critical points of approximations of the Dirichlet energy \`{a} la Sacks-Uhlenbeck are known to converge to harmonic maps in a suitable sense. However, we show that not every harmonic map can be approximated by critical points of such…

We show that a minimal dynamical system $(X,\mathbb{Z})$ on a compact metric $X$ with mdim$X=d$ admits for every natural $k>d$ an equivariant map to the shift $([0,1]^k)^{\mathbb{Z}}$ such that each fiber of this map contains at most…

A general ansatz in Renormalization Theory, already established in many important situations, states that exponential convergence of renormalization orbits implies that topological conjugacies are actually smooth (when restricted to the…

We extend the theory of quasipotentials in dynamical systems by calculating, within a broad class of period-doubling maps, an exact potential for the critical fluctuations of pitchfork bifurcations in the weak noise limit. These…

4-harmonic and ES-4-harmonic maps are two generalizations of the well-studied harmonic map equation which are both given by a nonlinear elliptic partial differential equation of order eight. Due to the large number of derivatives it is very…