Related papers: Normal forms of hyperbolic logarithmic transseries

Using techniques from ergodic theory and symbolic dynamics, we derive statistical limit laws for real valued functions on hyperbolic groups. In particular, our results apply to convex cocompact group actions on $\text{CAT}(-1)$ spaces, and…

Here, Darboux's classical results about transformations with differential substitutions for hyperbolic equations are extended to the case of parabolic equations of the form $L u = \big(D^2_{x} + a(x,y) D_x + b(x,y) D_y + c(x,y)\big)u=0$. We…

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the…

Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…

In this article we formulate and prove sufficient conditions for the existence of trajectories of nonstationary periodic solutions of autonomous Hamiltonian systems in a neighbourhood of equilibria. It is worth pointing out that assumptions…

This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…

We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…

We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…

We establish Liouville type theorems in the whole space and in a half-space for parabolic problems without scale invariance. To this end, we employ two methods, respectively based on the corresponding elliptic Liouville type theorems and…

In this article, we present a landing theorem for periodic dynamic rays for transcendental entire maps which have bounded post-singular sets, by using standard hyperbolic geometry results.

We study the approximation of parabolic Hamilton-Jacobi-Bellman (HJB) equations in bounded domains with strong Dirichlet boundary conditions. We work under the assumption of the existence of a sufficiently regular barrier function for the…

A new technique for proving fixed point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded representation in a real or complex Hilbert space is…

We analyse the fine convergence properties of one parameter families of hyperbolic metrics, on a fixed underlying surface, that move always in a horizontal direction, i.e. orthogonal to the action of diffeomorphisms.

We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…

This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary…

We present a unified approach to a couple of central limit theorems for radial random walks on hyperbolic spaces and time-homogeneous Markov chains on the positive half line whose transition probabilities are defined in terms of the Jacobi…

We present a complete algorithm that computes all hypergeometric solutions of homogeneous linear difference equations and rational solutions of parameterized linear difference equations in the setting of $\Pi\Sigma^*$-fields. More…

The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…

Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…

In this paper, we study the logarithmic stability for the hyperbolic equations by arbitrary boundary observation. Based on Carleman estimate, we first prove an estimate of the resolvent operator of such equation. Then we prove the…