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We consider a robust class of random non-uniformly expanding local homeomorphisms and H\"older continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and…
The phase space of an integrable, volume-preserving map with one action and $d$ angles is foliated by a one-parameter family of $d$-dimensional invariant tori. Perturbations of such a system may lead to chaotic dynamics and transport. We…
Under the natural action of the pure mapping class group of a surface of genus at least three, we show that any global fixed point in the low-dimensional deformation space of the surface group corresponds to the trivial representation. A…
We consider linearly stable elliptic fixed points for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. Morbidelli and Giorgilli have proved a theorem of stability over…
A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is…
We study a relationship between rational proper maps of balls in different dimensions and strongly plurisubharmonic exhaustion functions of the unit ball induced by such maps. Putting the unique critical point of this exhaustion function at…
We study normal forms of germs of singular real-analytic Levi-flat hypersurfaces. We prove the existence of rigid normal forms for singular Levi-flat hypersurfaces which are defined by the vanishing of the real part of complex…
We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and…
The paper deals with dynamics of expanding Lorenz maps, which appear in a natural way as Poincar\`e maps in geometric models of well-known Lorenz attractor. Using both analytical and symbolic approaches, we study connections between…
In this paper we provide novel results on the infinite level normal form and orbital normal form classifications of nonlinear Eulerian and rotational vector fields with two pairs of non-resonant imaginary modes. We use the method of…
Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by…
We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image…
In this paper, we present an approach to enhance and improve the current normal map rendering technique. Our algorithm is based on semi-discrete Optimal Mass Transportation (OMT) theory and has a solid theoretical base. The key difference…
We study the group of volume-preserving diffeomorphisms on a manifold. We develop a general theory of implicit generating forms. Our results generalize the classical formulas for generating functions of symplectic twist maps.
We present a general analysis of the bifurcation sequences of periodic orbits in general position of a family of reversible 1:1 resonant Hamiltonian normal forms invariant under $\Z_2\times\Z_2$ symmetry. The rich structure of these…
On a Riemannian surface, the energy of a map into a Riemannian manifold is a conformal invariant functional, and its critical points are the harmonic maps. Our main result is a generalization of this theorem when the starting manifold is…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
It is shown that a Hamiltonian system in the neighbourhood of an equilibrium may be given a special normal form in case the eigenvalues of the linearized system satisfy non--resonance conditions of Melnikov's type. The normal form possesses…
We construct on $\R^{2d}$, for any $d \geq 3$, smooth Hamiltonians having an elliptic equilibrium with an arbitrary frequency, that is not accumulated by a positive measure set of invariant tori. For $d\geq 4$, the Hamiltonians we construct…
We present a proof of the existence of a renormalization fixed point for Lorenz maps of the simplest non-unimodal combinatorial type ({0,1},{1,0,0}), and with a critical point of arbitrary order rho>1.