Related papers: Isolated, slowly evolving, and dynamical trapping …
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data analysis. These filtrations quantify, in a forward direction,…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a flat metric with several cone-type…
Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…
This work investigates the out-of-equilibrium dynamics of dipole and higher-moment conserving systems with long-range interactions, drawing inspiration from trapped ion experiments in strongly tilted potentials. We introduce a hierarchical…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in $D$ dimensions coupled to a $q$-form field and positive cosmological constant. We show that…
The requirement that a trapped spacetime domain forms in finite time for distant observers is logically possible and sometimes unavoidable, but its consequences are not yet fully understood. In spherical symmetry, the characterization of…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…
Dynamical horizons are considered in full, non-linear general relativity. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local, the energy flux is positive…
We present a general formalism which allows us to derive the evolution equations describing one-dimensional (1D) and isotropic 2D interfacelike systems, that is based on symmetries, conservation laws, multiple scale arguments, and exploits…
This thesis deals with the formulation and analysis of two systems of conservation laws defined on two complementary intervals and coupled by some moving interface as a single infinite-dimensional port-Hamiltonian system. This approach may…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
The dynamics of apparent and event horizons of various black hole spacetimes, including those containing distorted, rotating and colliding black holes, are studied. We have developed a powerful and efficient new method for locating the…
We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event…
We derive the higher dimensional generalization of Penrose--Tod equation describing past horizon in Robinson--Trautman spacetimes with a cosmological constant and pure radiation. Existence of its solutions in $D>4$ dimensions is proved…