Related papers: Dani's Work on Dynamical Systems on Homogeneous Sp…
From the sandpoint of neural network dynamics we consider dynamical system of special type pesesses gradient (symmetric) and Hamiltonian (antisymmetric) flows. The conditions when Hamiltonian flow properties are dominant in the system are…
This special issue collects contributions from the participants of the "Information in Dynamical Systems and Complex Systems" workshop, which cover a wide range of important problems and new approaches that lie in the intersection of…
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…
We review the field of the glass transition, glassy dynamics and aging from a statistical mechanics perspective. We give a brief introduction to the subject and explain the main phenomenology encountered in glassy systems, with a particular…
A theoretical treatment of deeply supercooled liquids is difficult because their properties emerge from spatial inhomogeneities that are self-induced, transient, and nanoscopic. I use computer simulations to analyse self-induced static and…
We prove analogs of the logarithm laws of Sullivan and Kleinbock-Margulis in the context of unipotent flows. In particular, we prove results for horospherical actions on homogeneous spaces $G/\Gamma$. We describe some relations with…
A central theme in Iachello's quest for understanding simple ordered patterns in complex quantum systems, is the concept of dynamical symmetry. Relying on his seminal contributions, we present further generalization of this notion to that…
We consider concepts centered around modal analysis, data science, network science, and machine learning to reveal the essential dynamics from high-dimensional fluid flow data and operators. The presentation of the material herein is…
A few remarks on integrable dynamical systems inspired by discussions with Jurgen Moser and by his work.
We will prove an S-arithmetic version of a theorem of Dani-Margulis on the convergence of ergodic averages of a given bounded continuous function, when the initial point is outside certain compact subsets of the singular set associated to…
In the 1960s and 1970s a large part of the theory of dynamical systems concerned the case of uniformly hyperbolic or Axiom A dynamical system and abstract ergodic theory of smooth dynamical systems. However since around 1980 an emphasize…
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…
Interest in the dynamical arrest leading to a fluid --> solid transition in thermal and athermal systems has led to questions about the nature of these transitions. These jamming transitions may be dependent on the influence of extended…
Dark energy is one of the deepest puzzles in modern cosmology, and mounting evidence suggests that it is not just a cosmological constant but a genuinely dynamical component. Although cosmology and dynamical systems theory emerged from…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…
The aim of this report is to review a theoretical approach that has been proposed recently to describe dynamic fluctuations in glassy systems (work in collaboration with H. Castillo, C. Chamon, P. Charbonneau, J. L. Iguain, M. Kennett, D.…
The dynamical properties of classical fluids at pico-liter scale attract experimentally and theoretically much attention in the soft-matter and biophysics communities, due to the appearance of the microfluidics, also called 'lab-on-a-chip',…
The present volume is a Festschrift for Mike Keane, on the occasion of his 65th birthday on January 2, 2005. It contains 29 contributions by Mike's closest colleagues and friends, covering a broad range of topics in Dynamics and…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…