Related papers: A Lax Functorial Definition of Open Dynamics
Dynamical systems---by which we mean machines that take time-varying input, change their state, and produce output---can be wired together to form more complex systems. Previous work has shown how to allow collections of machines to…
We revisit the theory of normal forms for non-uniformly contracting dynamics. We collect a number of lemmas and reformulations of the standard theory that will be used in other projects.
Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…
It has been an open question as to whether the Modular Structural Operational Semantics framework can express the dynamic semantics of call/cc. This paper shows that it can, and furthermore, demonstrates that it can express the more general…
Like any other logical theory, domain descriptions in reasoning about actions may evolve, and thus need revision methods to adequately accommodate new information about the behavior of actions. The present work is about changing action…
These are pedagogical lecture notes on hydrodynamic fluctuations in normal relativistic fluids. The lectures discuss correlation functions of conserved densities in thermal equilibrium, interactions of the hydrodynamic modes, an effective…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
We consider some natural connections which arise between right-flat (p, q) paraconformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a "Lax p-tuple" of linear differential operators,…
Starting from a microscopic approach, we develop a covariant formalism to describe a set of interacting gases. For that purpose, we model the collision term entering the Boltzmann equation for a class of interactions and then integrate this…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
The use of non-deterministic functions is a distinctive feature of modern functional logic languages. The semantics commonly adopted is call-time choice, a notion that at the operational level is related to the sharing mechanism of lazy…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
We here discuss the process of opinion formation in an open community where agents are made to interact and consequently update their beliefs. New actors (birth) are assumed to replace individuals that abandon the community (deaths). This…
We consider extensions of the notion of topological transitivity for a dynamical system $(X,f)$. In addition to chain transitivity, we define strong chain transitivity and vague transitivity. Associated with each there is a notion of…
The conventional economic approaches explore very little about the dynamics of the economic systems. Since such systems consist of a large number of agents interacting nonlinearly they exhibit the properties of a complex system. Therefore…
A dynamic logic ${\mathbf B}$ can be assigned to every automaton ${\mathcal A}$ without regard if ${\mathcal A}$ is deterministic or nondeterministic. This logic enables us to formulate observations on ${\mathcal A}$ in the form of composed…
In this article we provide a model-independent definition of the concept of lax $2$-functors from $(\infty,2)$-category theory and show that it agrees with the existing and widely used combinatorial model for those in terms of…
It is shown how the macroscopic non-equilibrium dynamics of a class of systems whose microscopic stochastic dynamics involves disordered and frustrated but range-free interactions can be well described by closed deterministic flow…