Related papers: Space of initial values of a map with a quartic in…

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_\infty$-invariant and concentrated on a single…

This paper focuses on using the first curvature $\kappa(t)$ of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems [Y. Wang, H. Sun, Y. Song et al.,…

This paper is devoted to study the topological invariance of several non-uniform hyperbolicity conditions of one-dimensional maps. In contrast with the case of maps with only one critical point, it is known that for maps with several…

In this paper we investigate the distribution of the set of values of a linear map at integer points on a quadratic surface. In particular we show that this set is dense in the range of the linear map subject to certain algebraic conditions…

We consider maps which preserve functions which are built out of the invariants of some simple vector fields. We give a reduction procedure, which can be used to derive commuting maps of the plane, which preserve the same symplectic form…

We consider the ring of invariants of n points on the projective line. The space (P^1)^n // PGL_2 is perhaps the first nontrivial example of a Geometry Invariant Theory quotient. The construction depends on the weighting of the n points.…

We show that the spatial increments of the KPZ fixed point starting from arbitrary initial data, exhibit strong quantitative comparison against rate two Brownian motion on compacts. The above estimates are uniform in the initial data…

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…

We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.

In a 1979 paper, K. Okamoto introduced the space of initial values for the six Painlev\'e equations and their associated Hamiltonian systems, showing that these define regular initial value problems at every point of an augmented phase…

We describe the construction of a geometric invariant characterising initial data for the Kerr-Newman spacetime. This geometric invariant vanishes if and only if the initial data set corresponds to exact Kerr-Newman initial data, and so…

In this paper, we investigate several properties of the solution maps of variational inequalities with polynomial data. First, we prove some facts on the $R_0$-property, the local boundedness, and the upper semicontinuity of the solution…

We construct 9-parameter and 13-parameter dynamical systems of the plane which map bi-quadratic curves to other bi-quadratic curves and return to the original curve after two iterations. These generalize the QRT maps which map each such…

This work numerically examines the temporal and spectral properties of a quadratic map. The quadratic map described in this study has quadratic non-linearity, and its theoretical analysis poses a challenge. Additionally, this map can be…

We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of…

We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where…

Time reversal symmetric triangular maps of the unit square are introduced with the property that the time evolution of one of their two variables is determined by a piecewise expanding map of the unit interval. We study their statistical…

Let $C/K$ be a smooth plane quartic over a discrete valuation field. We characterize the type of reduction (i.e. smooth plane quartic, hyperelliptic genus 3 curve or bad) over $K$ in terms of the existence of a special plane quartic model…

The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We…

Hard disks systems are often considered as prototypes for simple fluids. In a statistical mechanics context, the hard disk configuration space is generally quotiented by the action of various symmetry groups. The changes in the topological…