Related papers: A Lax Functorial Definition of Open Dynamics
We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium…
The concepts of fuzzy objects and their classes are described that make it possible to structurally represent knowledge about fuzzy and partially-defined objects and their classes. Operations over such objects and classes are also proposed…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
This paper defines antifragility for dynamical systems as convexity of a newly introduced "logarithmic rate". It shows how to compute this rate for positive linear systems, and it interprets antifragility in terms of pulsed alternations of…
This is a light survey article about the origins of contact and symplectic topology in dynamics and the more recent developments in the field. In lieu of formulas, numerous anecdotes are given.
We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…
We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…
We present theoretical and practical results on the order theory of lattices of functions, focusing on Galois connections that abstract (sets of) functions - a topic known as higher-order abstract interpretation. We are motivated by the…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
A notion of time is fundamental in the study of dynamical systems. Time arises as a standalone dynamical system and also in solutions or trajectories as a special kind of map between systems. We characterize time by a universal property and…
We define a Lax operator as a monic pseudodifferential operator $L(\partial)$ of order $N\geq 1$, such that the Lax equations $\dfrac{\partial L(\partial)}{\partial t_k}=[(L^{\frac kN}(\partial))_+,L(\partial)]$ are consistent and non-zero…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
A definition for functions of multidimensional arrays is presented. The definition is valid for third-order tensors in the tensor t-product formalism, which regards third-order tensors as block circulant matrices. The tensor function…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
A simple review by a linguist, citing many articles by physicists: Quantitative methods, agent-based computer simulations, language dynamics, language typology, historical linguistics
A new concept called biased derivative is proposed. It has a potential to better understand and model some aspects of dynamical systems associated with creating bubbles.
The work is devoted to constructing a wide class of differential-functional dynamical systems, whose rich algebraic structure makes their integrability analytically effective. In particular, there is analyzed in detail the operator Lax type…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…