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Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.
We prove the existence (and give a characterization) of a germ of complex analytic set left invariant by an abelian group of germs of holomorphic diffeomorphisms at a common fixed point.We also give condition that ensure that such a group…
The aim of this work is to study the analytic continuation of the doubly-periodic Barnes zeta function. By using a suitable complex integral representation as a starting point we find the meromorphic extension of the doubly periodic Barnes…
The possibility to study intermittency in a single event of high multiplicity is investigated in the framework of the $\alpha-$model. It is found that, for cascade long enough, the dispersion of intermittency exponents obtained from…
In this paper we give moduli of analytic classification for parabolic Dulac i.e. almost regular germs. Dulac germs appear as first return maps of hyperbolic polycycles. Their moduli are given by a sequence of Ecalle-Voronin-like germs of…
The theoretical description of the heterogeneous nucleation kinetics is presented. This description takes into account the perturbation of the vapor phase initiated by the growing droplets. The form of the density profile around the growing…
We study several different notions of algebraicity in use in stable homotopy theory and prove implications between them. The relationships between the different meanings of algebraic are unexpectedly subtle, and we illustrate this with…
We give conditions under which a germ of a holomorphic mapping in $\Bbb C^N$, mapping an irreducible real algebraic set into another of the same dimension, is actually algebraic. Let $A\subset \bC^N$ be an irreducible real algebraic set.…
In this paper we prove an abstract theorem which can be used to study the existence of solitons for various dynamical systems described by partial differential equations. We also give an idea of how the abstract theorem can be applied to…
Systems of germs of sets in infinite-dimensional spaces are introduced and studied. Such a system corresponds to a local zero-set of an ideal of the ring of analytic functions of infinite number of variables. Conversely, this system of…
We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent…
It is known that there is at least an invariant analytic curve passing through each of the components in the complement of nodal singularities, after the reduction of singularities of a germ of singular foliation in ${\mathbb C}^2,0$}.…
We prove that the preimage of a germ of a singular analytic hypersurface under a germ of a finite holomorphic map $g: (\mathbb{C}^n,0) \rightarrow (\mathbb{C}^n,0)$ is again singular. This provides a generalization of previous results of…
The existence of travelling waves for a model of concentration waves of bacteria is investigated. The model consists in a kinetic equation for the biased motion of cells following a run-and-tumble process, coupled with two…
We study the algebraic dynamics of endomorphisms of projective varieties. First, we characterize their iterated images, i.e. the intersection of the images of their iterates. Next, we explore the Stein factorizations of the iterates,…
We recall fundamental aspects of the pluriclosed flow equation and survey various existence and convergence results, and the various analytic techniques used to establish them. Building on this, we formulate a precise conjectural…
We study random holomorphic endomorphisms of P^k(C). This article is the second part of arXiv:1205.1601
We show a continuity result for the Weyl pseudometric on subshifts which are generated by model sets. This fact is then used for multiple constructions of subshifts that exhibit different behavior regarding entropy, amorphic complexity and…
We consider H\"older continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $M$. We obtain several results for this setting. If a cocycle is bounded in…
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…