Related papers: Geometric pressure in real and complex 1-dimension…

Surfaces of finite geometric type are complete, immersed into the tree-dimensional Euclidean space with finite total curvature and Gauss map extending to an oriented compact surface as a smooth branched covering map over the unit sphere of…

Some classical aspects of Metric-Affine Gravity are reviewed in the context of the $F^{(n)}(R)$ type models (polynomials of degree $n$ in the Riemann tensor) and the topologically massive gravity. At the non-perturbative level, we explore…

In this paper we study the geometry of a certain class of compact dynamical horizons with a time-dependent induced metric in locally rotationally symmetric class II spacetimes. We first obtain a compactness condition for embedded…

It is known that all uniformly expanding dynamics $f: M \rightarrow M$ have no phase transition with respect to a H\"older continuous potential $\phi : M \rightarrow \mathbb{R}$, in other words, the topological pressure function $\mathbb{R}…

We investigate the possibility that the spatial dependency of stress in generalized Newtonian flow systems is a function of the applied pressure field and the conduit geometry but not of the fluid rheology. This possibility is well…

Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of "equipartition"…

Consider a rational map $f$ of degree at least 2 acting on its Julia set $J(f)$, a H\"older continuous potential $\phi: J(f)\rightarrow \R$ and the pressure $P(f,\phi). In the case where $\sup_{J(f)}\phi<P(f,phi)$, the uniqueness and…

Let $f, g:S^1\to S^1$ be two $C^3$ critical homeomorphisms of the circle with the same irrational rotation number and the same (finite) number of critical points, all of which are assumed to be non-flat, of power-law type. In this paper we…

Using Thurston's characterization of postcritically finite rational functions as branched coverings of the sphere to itself, we give a new method of constructing new conformal dynamical systems out of old ones. Let $f(z)$ be a rational map…

Inspired by group cohomology, we define several coarse topological invariants of metric spaces. We define the coarse cohomological dimension of a metric space, and demonstrate that if G is a countable group, then the coarse cohomological…

In the context of geodesic flows of noncompact negatively curved manifolds, we propose three different definitions of entropy and pressure at infinity, through growth of periodic orbits, critical exponents of Poincar\'e series, and entropy…

The topological complexity ${\sf TC}(X)$ is a homotopy invariant of a topological space $X$, motivated by robotics, and providing a measure of the navigational complexity of $X$. The topological complexity of a connected sum of real…

In this article, the historic set is divided into different level sets and we use topological pressure to describe the size of these level sets. We give an application of these results to dimension theory. Especially, we use topological…

We obtain an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness…

We consider here the discrete time dynamics described by a transformation $T:M \to M$, where $T$ is either the action of shift $T=\sigma$ on the symbolic space $M=\{1,2,...,d\}^\mathbb{N}$, or, $T$ describes the action of a $d$ to $1$…

Let $K$ be a number field, and $\varphi_{1},\ldots,\varphi_{g}\in K(t)$ be finitely many rational maps, each of degree at least $2$. We first show that for generic finite sets $\mathcal{A}_{1},\ldots,\mathcal{A}_{g}$ consisting entirely of…

We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…

In this paper we provide a bridge between classical results concerning discrete dynamical systems and dynamical systems governed by nonsmooth vector fields. In fact, we obtain a set of piecewise smooth vector field trajectories where the…

In this note, we investigate the tree pressure for multi-modal interval maps with a certain class of hyperbolic and non-exceptional upper semi-continuous functions. In particular, we obtain a generalized version of Corollary 2.2 in the…

We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points…