Related papers: Quantitative statistical properties of two-dimensi…
We study ergodic properties of certain piecewise smooth two-dimensional systems by constructing countable Markov partitions. Using thermodynamic formalism we prove exponential decay of correleations.
We present the general properties of dynamic dissipative fluid distribution endowed with hyperbolical symmetry. All the equations required for its analysis are exhibited and used to contrast the behavior of the system with the spherically…
There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power…
Although the hyperbolic metric possesses many remarkable properties, it is not defined on arbitrary subdomains of $\mathbb{R}^n$ with $n \geq 2$. This article introduces a new hyperbolic-type metric that provides an alternative approach to…
The notion of semi-classical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is…
We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space,…
We provide two robust examples of globally partially hyperbolic systems with a multi one-dimensional center splitting, for which all Gibbs u-states are hyperbolic and the number of physical measures is fixed. In the second example, the…
In this note we describe some results concerning non-relativistic quantum systems at positive temperature and density confined to macroscopically large regions of physical space which are under the influence of some local, time-dependent…
We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a transition at some finite temperature, from a type of short range order to a fundamentally different…
We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time…
Arnold's diffusion in quasi integrable hamiltonian systems occurs in exponentially large time. We study an initially hyperbolic system which admits diffusion in polynomial time.
In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for…
Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is…
We prove stability for a coefficient determination problem for a two velocity 2x2 system of hyperbolic PDEs in one space dimension.
Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. We characterize, for subgroups of G, when…
The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy…
This thesis presents a set of studies on atomic systems where quantum effects are particularly relevant. These studies have been developed by applying a variety of tools from many-body physics. First of all, we have studied the prospects…
In this paper, we introduce the concept of completely linear degeneracy for quasilinear hyperbolic systems in several space variables, and then get an interesting property for multidimensional hyperbolic conservation laws. Some examples and…