Related papers: Fold singularities of nonsmooth and slow-fast dyna…

Discontinuous piecewise differential systems exhibit dynamical behaviors with no counterpart in smooth systems, particularly in the presence of nonsmooth switching structures. In this work, we extend previous results for systems separated…

Topological singularities are ubiquitous in many areas of physics. Polarization singularities are locations at which an aspect of the polarization ellipse of light becomes undetermined or degenerate. At C points the orientation of the…

We study homogeneous cosmological models featuring shift-symmetric scalar fields (or, superfluids) in relative motion. In the presence of anisotropy this universe generally features rotation, in the sense that the principal axes of…

The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…

The cyclicity problem, crucial in analyzing planar vector fields, consists in estimating the number of limit cycles emanating from monodromic singularities. Traditionally, this estimation relies on Lyapunov coefficients. However, in…

We prove that oriented and standard shadowing properties are equivalent for topological flows on closed surfaces with the nonwandering set consisting of the finite number of critical elements (i.e., singularities or closed orbits).…

In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…

In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this…

The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads…

The dynamics of singularity formation on the interface between two ideal fluids is studied for the Kelvin-Helmholtz instability development within the Hamiltonian formalism. It is shown that the equations of motion derived in the small…

The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is…

It is revealed that distribution functions of practical gases relate to singularities and such singularities can, with molecular motion, spread to the entire region of interest. It is also shown that even common continuous distribution…

We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…

The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…

This paper develops fundamental mathematical theory for second-order Filippov systems. These are discontinuous ordinary differential equations with solutions defined in the sense of Filippov, and whose first Lie derivatives vary…

The slow viscous flow through a doubly-periodic array of cylinders does not have an analytical solution. However, as a reduced model for the flow within fibrous porous media, this solution is important for many real-world systems. We…

We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in…

The conformations and dynamics of semiflexible filaments subject to a homogeneous external (gravitational) field, e.g., in a centrifuge, are studied numerically and analytically. The competition between hydrodynamic drag and bending…

We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling…

Particle sedimentation in the vicinity of a fixed horizontal vortex with time-dependent intensity can be chaotic, provided gravity is sufficient to displace the particle cloud while the vortex is off or weak. This "stretch, sediment and…