Related papers: Lie families: theory and applications

The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

This paper provides a practical approach to stochastic Lie systems, i.e. stochastic differential equations whose general solutions can be written as a function depending only on a generic family of particular solutions and some constants…

We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal…

We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted…

This article is the third in a series the aim of which is to use Lie group theory to obtain exact analytic solutions of Delay Ordinary Differential Systems (DODSs). Such a system consists of two equations involving one independent variable…

We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed…

We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable…

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent…

Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…

We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…

In this paper we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on 1 function of 1 variable. We describe linearization of such systems and their integration via…

It is proved that the members of the Riccati hierarchy, the so-called Riccati chain equations, can be considered as particular cases of projective Riccati equations, which greatly simplifies the study of the Riccati hierarchy. This also…

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…

A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…

In the paper, elements of the system theory of time are presented, mathematical models for time are constructed, and various properties are deduced from the main principles of the system theory of time. This theory is a far-reaching…