相关论文: Complex dynamics in several variables

In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…

Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a…

High-Dimensional Dynamic Factor Models are presented in detail: The main assumptions and their motivation, main results, illustrations by means of elementary examples. In particular, the role of singular ARMA models in the theory and…

We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…

Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…

These notes were written for a set of three lectures given in a school at the Max Planck Institute for the Physics of Complex Systems in October/2017 before the workshop "Critical Stability of Quantum Few-Body Systems". These lectures are…

The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…

Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole…

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…

Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. So far kinetic constraints have been introduced in idealised models aiming to capture…

These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…

These are notes to accompany my lectures at the $2024$ "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our understanding of two and three dimensional dynamical systems,…

These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…

The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…

The main purpose of this expository note is to give a short account of the recent developments in mathematical wave kinetic theory. After reviewing the physical theory, we explain the importance of the notion of a scaling law, which…

The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.

We investigate dynamics of scalar field with non-minimal kinetic term. Nontrivial behavior of the field in the vicinity of singular points of kinetic term is observed. In particular, the singular points could serve as attractor for…

A case for the teaching of classical thermodynamics with an explicit time variable, with phenomena involving changes in time, is made by presenting and solving a exercise in textbook style, and pointing out that a solution accords with…

This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…

These notes provide an introduction to and a survey on recent results about the long-time behaviour of solutions to hyperbolic partial differential equations with time-dependent coefficients. Particular emphasis is given also to questions…