Related papers: Conley-Morse-Forman theory for combinatorial multi…

We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…

In this paper we study continuous parametrized families of dissipative flows, which are those flows having a global attractor. The main motivation for this study comes from the observation that, in general, global attractors are not robust,…

Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered,…

The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters…

A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…

Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…

The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…

We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials as dynamical systems. This lays the foundation for classification results of more general classes of Newton maps. A fundamental…

This paper is concerned with the Morse theory of attractors for semiflows on complete metric spaces. First, we construct global Morse-Lyapunov functions for Morse decompositions of attractors. Then we extend some well known deformation…

We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the…

We survey interactions between the topology and the combinatorics of complex hyperplane arrangements. Without claiming to be exhaustive, we examine in this setting combinatorial aspects of fundamental groups, associated graded Lie algebras,…

This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…

We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…

Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…

This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…

We detect, by using symplectic topology, invariant measures with large rotation vectors for a class of Hamiltonian flows.

In this note, we introduce the concept of momentumly closed forms. A nondegenerate momentumly closed two-form defines a moment map that generalizes the classical notion associated with symplectic forms. We then develop an extended theory of…

For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse…

This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order…

We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…