Related papers: On the stable set of an analytic gradient flow
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…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
This paper clarifies the main research methods and ideas of the thesis [1,2,4]. The special calculation process is also realized by corresponding computer algorithm. Finally, we introduce zero rows sum case and give the corresponding…
The topological dynamics of the horocyclic flow h_R on the unit tangent bundle of a geometrically finite hyperbolic surface is well known. In particular on such a surface the flow h_R is minimal or the minimal sets are the periodic orbits.…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
For any real-valued stochastic process X with c\`adl\`ag paths we define non-empty family of processes, which have finite total variation, have jumps of the same order as the process X and uniformly approximate its paths: This allows to…
If the nodes of a graph are considered to be identical barrels - featuring different water levels - and the edges to be (locked) water-filled pipes in between the barrels, consider the optimization problem of how much the water level in a…
We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation…
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…
The phenomenon of stable persistent currents is central to the studies of superfluidity in a range of physical systems. While all of the previous theoretical studies of superfluid flows in annular geometries concentrated on conservative…
With the tracking condition, the stability of quintessence solutions are examined. It is found that there is only one physically relevant fixed point for the system generically. Two specific examples of quintessence potentials are worked…
In this paper, we investigate the embeddings for topological flows. We prove an embedding theorem for discrete topological system. Our results apply to suspension flows via constant function, and for this case we show an embedding theorem…
Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This makes the analysis of standard optimization methods such as…
This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and…
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the analysis is based on the so-called iterative time profiles,…
The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for…
We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
This paper continues the study of equilibria for flows over time in the fluid queueing model recently considered by Koch and Skutella [10]. We provide a constructive proof for the existence and uniqueness of equilibria in the case of a…