Related papers: Miquel dynamics for circle patterns
We study the over-damped dynamics of individual one-dimensional elastic filaments subjected to a chiral active force which propels each point of the filament at a fixed angle relative to the tangent vector of the filament at that point.…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this…
Vertical thermal convection system exhibits weak turbulence and spatio-temporally chaotic behaviour. In this system, we report seven equilibria and 26 periodic orbits, all new and linearly unstable. These orbits, together with four…
Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…
Recent experimental studies have shown that confinement can profoundly affect self-organization in semi-dilute active suspensions, leading to striking features such as the formation of steady and spontaneous vortices in circular domains and…
In recent years there have been significant advances in the study of many-body interactions between atoms and light confined to optical cavities. One model which has received widespread attention of late is the Dicke model, which under…
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we…
We get three basic results in algebraic dynamics: (1). We give the first algorithm to compute the dynamical degrees to arbitrary precision. (2). We prove that for a family of dominant rational self-maps, the dynamical degrees are lower…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
We study discrete-time random dynamical systems where each fibre map is an orientation-preserving homeomorphism of the circle. We prove that the existence of a random periodic cycle with period at least two implies that the random rotation…
We formulate the equations of fluid dynamics as an intersection-theoretic problem on an infinite-dimensional symplectic manifold naturally associated with spacetime. This perspective separates the structures determined by the equation of…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
This paper introduces dynamic mechanism design in an elementary fashion. We first examine optimal dynamic mechanisms: We find necessary and sufficient conditions for perfect Bayesian incentive compatibility and formulate the optimal dynamic…
We analyze a new class of time-periodic nonreciprocal dynamics in interacting chaotic classical spin systems, whose equations of motion are conservative (phase-space-volume-preserving) yet possess no symplectic structure. As a result, the…
We study the quantum matrix algebra $R_{21}x_1x_2=x_2x_1 R$ and for the standard $2\times 2$ case propose it for the co-ordinates of $q$-deformed Euclidean space. The algebra in this simplest case is isomorphic to the usual quantum matrices…
A model equation has been proposed to describe bimodal features in vehicular traffic flows. The dynamics of the bimodal distribution reveals the existence of a fixed point that is connected to itself by a homoclinic trajectory. The…
We establish a new theoretical framework, based on a time-dependent mean field approach, to address the dynamics of the driven Dicke model. The joint evolution of both mean fields and quantum fluctuations gives rise to a rich and generally…
The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known to exhibit complicated, possibly chaotic…