Related papers: Dynamical properties of families of holomorphic ma…
Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold…
Short $\mathbb{C}^2$'s were constructed in [F] as attracting basins of a sequence of holomorphic automorphisms whose rate of attraction increases superexponentially. The goal of this paper is to show that such domains also arise naturally…
The conformational and dynamical properties of active self-propelled filaments/polymers are investigated in the presence of hydrodynamic interactions by both, Brownian dynamics simulations and analytical theory. Numerically, a discrete…
In vitro epithelial monolayers exhibit a rich repertoire of collective dynamical behaviours according to microenvironment mechanical features. We investigate the statistical and dynamical properties of human bronchial epithelial cell (HBEC)…
Equilibrium self-assembly and conventional materials processing techniques fall far short of mimicking dynamic self-actuating processes that are commonplace throughout biology. To bridge the gap between living and synthetic matter, we study…
We consider a family of stochastic models of evolving two-dimensional Young diagrams, given in terms of certain energies, with Gibbs invariant measures. `Static' scaling limits of the shape functions, under these Gibbs measures, have been…
Consider a holomorphic map $F: D \to G$ between two domains in ${\mathbb C}^N$. Let $\mathcal F$ denote a family of geodesics for the Kobayashi distance, such that $F$ acts as an isometry on each element of $\mathcal F$. This paper is…
The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of…
In this article, we develop a dynamical theory for what shall be called a skew product on the Berkovich projective line, $\phi_*: \mathbb{P}^1_{\text{an}}(K) \to \mathbb{P}^1_{\text{an}}(K)$ over a non-Archimedean field $K$. These functions…
Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been…
Given a surface $M$ and a Borel probability measure $\nu$ on the group of $C^2$-diffeomorphisms of $M$, we study $\nu$-stationary probability measures on $M$. We prove for hyperbolic stationary measures the following trichotomy: either the…
Two dimensional free surface flows in Hele-Shaw configurations are a fertile ground for exploring nonlinear physics. Since Saffman and Taylor's work on linear instability of fluid--fluid interfaces, significant effort has been expended to…
Topological defects in active liquid crystals can be confined by introducing gradients of activity. Here, we examine the dynamical behavior of two defects confined by a sharp gradient of activity that separates an active circular region and…
The aim of this manuscript is to understand the dynamics of products of nonnegative matrices. We extend a well known consequence of the Perron-Frobenius theorem on the periodic points of a nonnegative matrix to products of finitely many…
We prove a finite-dimensional moment map property for certain canonical relatively K\"ahler metrics on holomorphic fibrations, called optimal symplectic connections. We then relate the existence of zeroes of this moment map to the stability…
In a conservative and partially hyperbolic three-dimensional setting, we study three representative classes of diffeomorphisms: those homotopic to Anosov (or Derived from Anosov diffeomorphisms), diffeomorphisms in neighborhoods of the…
We study skew-maps given by a minimal homeomorphism on the basis and a cocycle of affine isometries on the fibers. We call such a map a cylindrical vortex. We extend to this setting some classical results of Atkinson, Besicovitch,…
In this paper we study holomorphic properties of infinite dimensional spin factors. Among the infinite dimensional Banach spaces with homogeneous open unit balls, we show that the spin factors are natural outlier spaces in which to ask the…
Consider a class of skew product transformations consisting of an ergodic or a periodic transformation on a probability space (M, B, m) in the base and a semigroup of transformations on another probability space (W,F,P) in the fibre. Under…
Let $M$ be a Kobayashi hyperbolic homogenous manifold. Let $\mathcal F$ be a holomorphic foliation on $M$ invariant under a transitive group $G$ of biholomorphisms. We prove that the leaves of $\mathcal F$ are the fibers of a holomorphic…