Related papers: Discrete dynamics and differentiable stacks

We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.

We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…

Multivariate oscillatory signals from complex systems often exhibit non-stationary dynamics and metastable regime structure, making dynamical interpretation challenging. We introduce a ``dynamical microscope'' framework that converts…

The space of directions is a notion of boundary associated to an arbitrary totally disconnected locally compact group. We explicitly calculate the space of directions of a group acting vertex transitively with compact open vertex…

This article reviews recent research on the collective dynamical behavior of colloids with dipolar or multipolar interactions. Indeed, whereas equilibrium structures and static self-assembly of such systems are now rather well understood,…

We show that every irreducible, simply connected curve on a toric affine surface X over the field of complex numbers is an orbit closure of a multiplicative group action on X. It follows that up to the action of the automorphism group…

We develop a robust foundation for studying the fundamental group(oid) in discrete homotopy theory, including: equivalent definitions and basic properties, the theory of covering graphs, and the discrete version of the Seifert-van Kampen…

We define a cocycle on the group of symplectic diffeomorphisms of a symplectic manifold and investigate its properties. The main applications are concerned with symplectic actions of discrete groups. For example, we give an alternative…

In Poincare-Wigner-Dirac theory of relativistic interactions, boosts are dynamical. This means that - just like time translations - boost transformations have non-trivial effect on internal variables of interacting systems. This is…

Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…

We study, numerically, the collective dynamics of self-rotating nonaligning particles by considering a monolayer of spheres driven by constant clockwise or counterclockwise torques. We show that hydrodynamic interactions alter the emergence…

For an action of the circle group $S^1$ on a compact oriented manifold with isolated fixed points, there is a claim that weights at the fixed points occur in pairs. This phenomenon holds for other types of $S^1$-manifolds, e.g., (almost)…

For a manifold M we define a structure on the group action of Diff(M) on the smooth functions on M which reduces to the usual differential geometry upon differentiation at zero along the one-parameter groups of Diff(M). This ``integrated…

We prove that a group $\Gamma$ admits a discrete topological (equivalently, smooth) action on some simply-connected 3-manifold if and only if $\Gamma$ has a Cayley complex embeddable -- with certain natural restrictions -- in one of the…

The homotopy groups of the (stabilized) group of invertible pseudodifferential operators of order zero acting on a closed manifold X are computed in terms of the K-theory of the cosphere bundle S*X. At the same time, we show that the…

We discover unexpected connections between packing configurations and rare fluctuations in dense systems of active particles subject to pulsation of size. Using large deviation theory, we examine biased ensembles which select atypical…

We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…

We investigate the correspondence between the geometry of a smooth compact Lie group action on a manifold $\mathrm{M}$ and the intrinsic smooth structure of the orbit space $\mathrm{M}/\mathrm{G}$. While the action on $\mathrm{M}$ is…

In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology,…

We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference…