相关论文: With Andrzej Lasota there and back again

This manuscript contains the lecture notes of the short courses given by one of us (F.Z.) at the summer school "Fundamental Problems in Statistical Physics XV", held in Brunico, Italy, in July 2021, and, just before that, at the summer…

The file contains PhD Dissertation by Oskar Jakub Szyma\'nski. This work ends his study at Doctoral School of Exact and Natural Sciences at Jagiellonian University where the Author has attended in years 2019-2024. The subject of the Thesis…

Poisson algebras have become an essential topic in mathematics with a rich structure and wide applicability. Despite numerous resources available on Poisson structures, the algebraic side of the story remains relatively less explored. This…

The present notes summarise the oligopoly dynamics lectures professor Lu\'is Cabral gave at the Bank of Portugal in September and October 2017. The lectures discuss a set industrial organisation problems in a dynamic environment, namely…

This is an extended version of my lecture at the LIII Cracow School of Theoretical Physics in Zakopane in which I presented the results of joint work with Piotr Bizo\'n concerning (in)stability of the three-dimensional anti-de Sitter…

We exhibit how the Rasiowa-Sikorski Lemma simplifies, in a sense, proofs of results that make use of the technique known as back-and-forth, often resulting in not very illustrative arguments. The first two sections seek to show one simple…

These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario derived from the solution…

We present an introduction to the study of chaos in discrete and continuous dynamical systems using the CAS Maxima. These notes are intended to cover the standard topics and techniques: discrete and continuous logistic equation to model…

These are lecture notes for a simple minicourse approaching the satistical properties of a dynamical system by the study of the associated transfer operator (considered on a suitable functions or measures spaces). The following questions…

Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…

Various kinematical quantities associated with the statistical properties of dynamical systems are examined: statistics of the motion, dynamical bases and Lyapunov exponents. Markov partitons for chaotic systems, without any attempt at…

These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…

This is an extended version of my Nobel Lecture, delivered on December $8^{th}$ 2021. I will recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe my contribution to the development of this…

Summary for the review talk on recent progress in the theoretical studies of electron momentum density distribution at the Sagamore XIII conference (Stare Jablonki, Poland; September 3-9, 2000).

Index: 1) Trajectories, distributions and path integrals. 2) Time-reversal and Equilibrium 3) Separation of timescales 4) Large Deviations 5) Metastability and dynamical phase transitions 6) Fluctuation Theorems and Jarzynski equality

Late Winter Lecture Notes, Short Course (10 hours) of Relativistic Astrophysics held at the Department of Physics and Astronomy of the University of Padova, March 13-17, 2017. Third version.

We discuss the role of ergodicity and chaos for the validity of statistical laws. In particular we explore the basic aspects of chaotic systems (with emphasis on the finite-resolution) on systems composed of a huge number of particles.

In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…

In this paper, we establish the law of the iterated logarithm for a wide class of non-stationary, continuous-time Markov processes evolving on Polish spaces. Specifically, our result applies to certain additive functionals of processes…

This is the abstract of a series of lectures given during the XIIIth School on Geometry and Physics, Bialystok (Poland), in July 2024. In this minicourse, we first examine the algebraic aspects of barycentric algebras. Then, we focus on…