Related papers: Poincar\'e maps and suspension flows: a categorica…

Polynomial functors are a categorical generalization of the usual notion of polynomial, which has found many applications in higher categories and type theory: those are generated by polynomials consisting a set of monomials built from sets…

Dynamics near the grazing manifold and basins of attraction for a motion of a material point in a gravitational field, colliding with a moving motion-limiting stop, are investigated. The Poincare map, describing evolution from an impact to…

Let $M$ be a smooth closed orientable manifold and $\mathcal{P}(M)$ the space of Poisson structures on $M$. We construct a Poisson bracket on $\mathcal{P}(M)$ depending on a choice of volume form. The Hamiltonian flow of the bracket acts on…

For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of their position. By assuming a global…

For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical…

In this paper we will prove that there exists a covariant functor from the category of schemes to the category of graphs. This functor provides a combination between algebraic varieties and combinatorial graphs so that the invariants…

In this master's thesis, we rigorously develop two frameworks of relational composition of systems using tools from category theory. The first framework addresses port-Hamiltonian systems, which are dynamical systems whose dynamics are…

We construct a topological invariant for a Morse-Smale flow on a 3-manifold and prove that the flows are topologically equivalent iff their invariants are same.

We present a simple viscous theory of free-surface flows in boundary layers, which can accommodate regions of separated flow. In particular this yields the structure of stationary hydraulic jumps, both in their circular and linear versions,…

We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies existence of an invariant. Conversely, a map with an…

We study the following functional equation that has arisen in the context of mechanical systems invariant under the Poincare algebra: \sum\limits_{i=1}^{n+1}\dfrac{\partial}{\partial x_{i}}\prod\limits_{j\neq i}f(x_{i}-x_{j}) =0,\qquad n…

A flow is a directed space structure on a homotopy type. It is already known that the underlying homotopy type of the realization of a precubical set as a flow is homotopy equivalent to the realization of the precubical set as a topological…

This article is devoted to the study of a $2$-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory…

For a finitely dominated Poincar\'e duality space $M$, we show how the author's total obstruction to the existence of a Poincar\'e embedding of the diagonal map $M \to M \times M$ relates to the Reidemeister trace of the identity map of…

In the present Letter we show that the concept of the generalized synchronization regime in discrete maps needs refining in the same way as it has been done for the flow systems [PRE, 84 (2011) 037201]. We have shown that\alkor{, in the…

Poincar\'e and Eisenstein series are building blocks for every type of modular forms. We define Poincar\'e series for Jacobi forms of lattice index and state some of their basic properties. We compute the Fourier expansions of Poincar\'e…

We study a number of categorical quasi-uniform structures induced by functors. We depart from a category $\mathcal{C}$ with a proper $(\mathcal{E}, \mathcal{M})$-factorization system, then define the continuity of a $\mathcal{C}$-morphism…

We study the asymptotical behaviour of iterates of piecewise contractive maps of the interval. It is known that Poincar\'e first return maps induced by some Cherry flows on transverse intervals are, up to topological conjugacy, piecewise…

This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…