Related papers: Dynamical systems in cosmology
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
This book is about dynamic programming and its applications in economics, finance, and adjacent fields. It brings together recent innovations in the theory of dynamic programming and provides applications and code that can help readers…
In recent years, by theory and observation cosmology has advanced substantially. Parameters of the concordance or $\Lambda$CDM cosmological model are given with unprecedented precision ("precision cosmology"). On the other side, 95% of the…
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…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
Cosmological models can be studied effectively using dynamical systems techniques. Starting from Brown's formulation of the variational principle for relativistic fluids, we introduce new types of couplings involving a perfect fluid, a…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
Two fundamental laws are needed for prediction in the universe: (1) a basic dynamical law and (2) a law for the cosmological initial condition. Quantum cosmology is the area of basic research concerned with the search for a theory of the…
These notes on modern cosmology were made with high school teachers and students in mind. Taking into account the lack of availability of time and classes that many teachers have nowadays in Brazil, often caused by having to comply with…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
This review is devoted to dynamical systems in fields of $p$-adic numbers: origin of $p$-adic dynamics in $p$-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems and…
Methods based on machine learning have recently made substantial inroads in many corners of cosmology. Through this process, new computational tools, new perspectives on data collection, model development, analysis, and discovery, as well…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
Cosmology contributes a good deal to the investigation of variation of fundamental physical constants. High resolution data is available and allows for detailed analysis over cosmological distances and a multitude of methods were developed.…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
In this paper we exploit the theory of the dynamical systems to study the dynamics of the standard cosmological model of the universe, which is known as the $\Lambda$CDM model. We assume that the matter content in our universe consists of…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers…
An introductory lectures on cosmology at ITEP Winter School for students specializing in particle physics are presented. Many important subjects are not covered because of lack of time and space but hopefully the lectures may serve as a…