Related papers: Asymptotically Conformal Fixed Points and Holomorp…

Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must…

This paper is devoted to the study of conformal maps of the unit disk $\mathbb{D}$ in the plane onto a bounded Jordan domain $G$. The main aim is to show that such a map is asymptotically symmetric if and only if $G$ is bounded by a…

We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost-additive continuous potentials $(\phi_n)_{n=1}^\infty$ on a topologically mixing subshift of finite type $X$ endowed itself with a metric associated…

For pullback attractors of asymptotically autonomous dynamical systems we study the convergences of their components towards the global attractors of the limiting semigroups. We use some conditions of uniform boundedness of pullback…

We discuss a new class of coordinate systems for a plane, which provide an analytical representation of arbitrary straightline, and then define the form of potential on the plane, under which the equations of motion of a mass point are…

We consider quasiconformal deformations of $\mathbb{C}\setminus\mathbb{Z}$. We give some criteria for infinitely often punctured planes to be quasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$. In particular, we characterize the…

This paper investigates asymptotic fixed point results for nonlinear contractions, with emphasis on Kirk-type theorems and their generalizations. A central difficulty in the literature has been the requirement that the mapping possesses a…

We study the asymptotic dynamics of maps which are piecewise contracting on a compact space. These maps are Lipschitz continuous, with Lipschitz constant smaller than one, when restricted to any piece of a finite and dense union of disjoint…

We give a new proof of the result that if f and g are transcendental entire functions, then the composite function f(g) has infinitely many fixed points. The method yields a number of generalization of this result. In particular, it extends…

We characterize when a compact, invariant, asymptotically stable attractor on a locally compact Hausdorff space is a strong deformation retract of its domain of attraction.

Inspired by biological systems, we introduce a general framework for quasi-static shape control of human-scale structures under slowly varying external actions or requirements. In this setting, shape control aims to traverse the stable…

The asymptotic Dirichlet problem for harmonic maps from the hyperbolic plane into conformally compact Einstein manifolds is used to give a holographic characterization of conformal geodesics on the boundary at infinity, in a way deeply…

M.Gromov extended the concepts of conformal and quasiconformal mapping to the mappings acting between the manifolds of different dimensions. For instance, any entire holomorphic function $ f: \Cn \to {\mathbb C}$ defines a mapping conformal…

Dynamists have been studying Hamiltonian systems for a long time. However, many physical systems are dissipative and do not preserve a symplectic form. This is the case, for example, with systems involving friction, which multiply the…

For a map f: X -> Y of quasi-compact quasi-separated schemes, we discuss quasi-perfection, that is, the right adjoint f^\times of the derived functor Rf_* respects small direct sums. This is equivalent to the existence of a functorial…

We describe the asymptotic behavior of the conformal modulus of an unbounded doubly-connected domain, non-symmetric with respect to the coordinate axes, when stretched in the direction of the abscissa axis with coefficient $H\to +\infty$.…

With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…

We define boundedness properties on the contractible fixed points set of the time-one map of an identity isotopy on a closed oriented surface with genus $g\geq1$. In symplectic geometry, a classical object is the notion of action function,…

We present a set of global invariants, called "mass integrals", which can be defined for a large class of asymptotically hyperbolic Riemannian manifolds. When the "boundary at infinity" has spherical topology one single invariant is…

In this paper we take an approach similar to that in [M] to establish a positive mass theorem for asymptotically hyperbolic spin manifolds admitting corners along a hypersurface. The main analysis uses an integral representation of a…