Related papers: 10 key problems in stellar dynamics: in retrospect
Lyapunov exponents (LEs) are key indicators of chaos in dynamical systems. In general relativity the classical definition of LE meets difficulty because it is not coordinate invariant and spacetime coordinates lose their physical meaning as…
After reviewing some of the basic concepts, nomenclatures and parametrizations of Astronomy, Astrophysics and Cosmology, we introduce a few central problems in Nuclear Astrophysics, including the hot-CNO cycle, helium burning in massive…
Supernova 1987A became a milestone in physics and astronomy. The most important things that have been learned from it, the most important problems yet to be solved and the prospects for learning important new physics from future…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
Our idea is to imitate Smale's list of problems, in a restricted domain of mathematical aspects of Celestial Mechanics. All the problems are on the n-body problem, some with different homogeneity of the potential, addressing many aspects…
We present an account of the state of the art in the fields explored by the research community invested in 'Modeling and Observing DEnse STellar systems'. For this purpose, we take as a basis the activities of the MODEST-17 conference,…
Radio pulsars provide us with some of the most stable clocks in the universe. Nevertheless several pulsars exhibit sudden spin-up events, known as glitches. More than forty years after their first discovery, the exact origin of these…
I discuss the development and resolution of the solar neutrino problem, as well as opportunities now open to us to extend our knowledge of main-sequence stellar evolution and neutrino astrophysics.
We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and…
These are remarks (mainly on the solar neutrinos) written in anticipation of 1996 - the year which can be crucial for the neutrino physics. Recent results on solar neutrinos are discussed. The topics include: (solar) model independent…
The textbook contains the problems in mechanics and special relativity for physics departments of universities. Many original problems were proposed by active scientists from the institutes of the Siberian Branch of Russian Academy of…
It is widely known that numerically integrated orbits are more precise than analytical theories for celestial bodies. However, calculation of the positions of celestial bodies via numerical integration at time $t$ requires the amount of…
This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov-Poisson…
Master equations are probably the most fundamental equations for anyone working in quantum optics in the presence of dissipation. In this context it is then incredibly useful to have efficient ways of coding and simulating such equations in…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
Errors in numerical simulations of gravitating systems can be magnified exponentially over short periods of time. Numerical shadowing provides a way of demonstrating that the dynamics represented by numerical simulations are representative…
We briefly review some constraints (Owing to the limited number of pages of present review, only a sub-sample of the topics discussed during the talk are briefly summarized. For the interested readers we are pleased to send them upon…
The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…
Invited Talk at {\sl ICNAPP}, Bangalore, India, Jan. 1994; {\sl Int. School on Cosmological Dark Matter}, Valencia, Oct. 1993; and Gran Sasso meeting on {\sl Solar Neutrino Problem: astrophysics or oscillations?}, march 1994.
Despite centuries of close association, statistics and astronomy are surprisingly distant today. Most observational astronomical research relies on an inadequate toolbox of methodological tools. Yet the needs are substantial: astronomy…