Related papers: Substitution maps in the Robba ring

We prove that the relative p-adic monodromy theorem holds over a dense open subset. Moreover, we establish the equivalence of the following two statements: the local constancy of the Newton polygon function associated with a de Rham local…

We show the equivalence of inverse problems for different dynamical systems and corresponding canonical systems. For canonical system with general Hamiltonian we outline the strategy of studying the dynamic inverse problem and procedure of…

We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…

In this paper, we define a certain Hodge-theoretic structure for an arbitrary variety X over the complex number field by using the theory of mixed Hodge module due to Morihiko Saito. We call it an arithmetic Hodge structure of X. It is…

I present a discussion of the hierarchy of Toda flows that gives center stage to the associated cocycles and the maps they induce on the $m$ functions. In the second part, these ideas are then applied to canonical systems; an important…

We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…

In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.

In a recent series of communications we have shown that the reordering problem of bosons leads to certain combinatorial structures. These structures may be associated with a certain graphical description. In this paper, we show that there…

In this note we describe instances where values of the $K$-theoretical regulator map evaluated on topological cycles equal entropies of topological actions by a group $\Gamma$. These entropies can also be described by determinants on the…

In this paper we lay the basis of the theory of rational modules of corings extending results on rational modules for coalgebras to the case of arbitrary ground rings. We apply these results mainly to categories of entwined modules (e.g.…

This paper is a sequel to our earlier paper "Wach modules and Iwasawa theory for modular forms" (arXiv: 0912.1263), where we defined a family of Coleman maps for a crystalline representation of the Galois group of Qp with nonnegative…

Translation surfaces can be defined in an elementary way via polygons, and arise naturally in in the study of various basic dynamical systems. They can also be defined as Abelian differentials on Riemann surfaces, and have moduli spaces…

We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann…

We explain the theory of refined cycle maps associated to arithmetic mixed sheaves. This includes the case of arithmetic mixed Hodge structures, and is closely related to work of Asakura, Beilinson, Bloch, Green, Griffiths, Mueller-Stach,…

We describe an approach to calculating the cohomology rings of stable map spaces. The method we use is due to Akildiz-Carrell and employs a C^*-action and a vector field which is equivariant with respect to this C^*-action. We give an…

The aim of this paper is to present an algebro-geometric approach to the study of the geometry of the moduli space of stable bundles on a smooth projective curve defined over an algebraically closed field $k$, of arbitrary characteristic.…

While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…

The monotonicity of entropy is investigated for real quadratic rational maps on the real circle $\mathbb{R}\cup\{\infty\}$ based on the natural partition of the corresponding moduli space $\mathcal{M}_2(\mathbb{R})$ into its monotonic,…

In this note we survey recent results on the extrinsic geometry of the Jacobian locus inside $\mathsf{A}_g$. We describe the second fundamental form of the Torelli map as a multiplication map, recall the relation between totally geodesic…

Berger asked the question \enquote{To what extent the preperiodic points of a stable $p$-adic power series determines a stable $p$-adic dynamical system} ? In this work we have applied the preperiodic points of a stable $p$-adic power…