Related papers: Dynamical systems in cosmology
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
This book provides an introduction to the field of star formation at a level suitable for graduate students or advanced undergraduates in astronomy or physics. The structure of the book is as follows. The first two chapters begin with a…
The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…
Physical cosmology tries to understand the Universe at large with its origin and evolution. Observational and experimental situations in cosmology do not allow us to proceed purely based on the empirical means. We examine in which sense our…
Cosmography represents an important branch of cosmology which aims to describe the universe without the need of postulating \emph{a priori} any particular cosmological model. All quantities of interest are expanded as a Taylor series around…
A simple description of the vacuum energy (cosmological constant) problem for non-experts is presented. Basic features of cosmology with non-zero vacuum energy are discussed. The astronomical data which indicate that the universe is filled…
General aspects about the thermodynamics of astrophysical systems are discussed, overall, those concerning to astrophysical systems in mutual interaction (or the called \emph{open astrophysical systems}). A special interest is devoted along…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
Based on the cosmological principle only, the method of describing the evolution of the Universe, called cosmography, is in fact a kinematics of cosmological expansion. The effectiveness of cosmography lies in the fact that it allows, based…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant applications in many areas: thermodynamics, cosmology, control theory, and neurogeometry, among others. In recent years there has been a great…
This entry is aimed at describing cloud physics with an emphasis on fluid dynamics. As is inevitable for a review of an enormously complicated problem, it is highly selective and reflects of the authors' focus. The range of scales involved,…
During the last three decades, there has been a growing realization among physicists and cosmologists that the relation between particle physics and cosmology may constitute yet another successful example of the unity of science. However,…
We discuss a number of fundamental aspects of modern cosmological concepts, from the phenomenological, observational, theoretical and epistemic points of view. We argue that the modern cosmology, despite a great advent, in particular in the…
We present a detailed investigation of the cosmological dynamics based on $\exp (-R/{\Lambda})$ gravity. We apply the dynamical system approach to both the vacuum and matter cases and obtain exact solutions and their stability in the finite…
Cosmology and high energy physics are two closely connected areas. In this lecture I present an example of their rich interplay.
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical…
A brief review of the present-day development of cosmology is presented for mixed physical audience. The universe history is briefly described. Unsolved problems are discussed, in particular, the mystery of the cosmological constant and…