Related papers: Resonances and Phase Locking Phenomena for Foliati…

We report experimental observation of the conversion of a phase-invariant nonlinear system into a phase-locked one via the mechanism of rocking [G. J. de Valcarcel and K. Staliunas, Phys. Rev. E 67, 026604 (2003)]. This conversion results…

Recent topological tools offer a powerful way to classify how phases of nonlinear bosonic resonators are organized. Yet, they remain incomplete. In particular, self-sustained oscillations in the form of limit cycles act as robust organizing…

Topological dislocations in otherwise periodic lattices represent global structural defects that, nevertheless, typically leave the lattice periodicity intact far from the dislocation. Such dislocations arise in diverse physical systems…

Torus leaves play a crucial role in the theory of foliations. For example non-taut foliations admit a torus leaf (see the article of Goodman). In this paper, we study all the foliations near a torus leaf, and try to understand why sometimes…

Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear…

Area-preserving nontwist maps are used to describe a broad range of physical systems. In those systems, the violation of the twist condition leads to nontwist characteristic phenomena, such as reconnection-collision sequences and shearless…

Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…

We consider a class of quasi-integrable Hamiltonian systems obtained by adding to a non-convex Hamiltonian function of an integrable system a perturbation depending only on the angle variables. We focus on a resonant maximal torus of the…

We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid…

The toroidal geometry of tokamaks and stellarators is known to play a crucial role in the linear physics of zonal flows, leading to e.g. the Rosenbluth-Hinton residual and geodesic acoustic modes. However, descriptions of the nonlinear…

We prove that if an area-preserving homeomorphism of the torus in the homotopy class of the identity has a rotation set which is a nondegenerate vertical segment containing the origin, then there exists an essential invariant annulus. In…

This article deals with directional rotational deviations for non-wandering periodic point free homeomorphisms of the 2-torus which are homotopic to the identity. We prove that under mild assumptions, such a homeomorphism exhibits uniformly…

The interplay between topological phases of matter and dissipative baths constitutes an emergent research topic with links to condensed matter, photonic crystals, cold atomic gases and quantum information. While recent studies suggest that…

Slow-fast dynamics and resonant phenomena can be found in a wide range of physical systems, including problems of celestial mechanics, fluid mechanics, and charged particle dynamics. Important resonant effects that control transport in the…

In this paper we consider an analog of the regions of instability for twist maps in the context of area preserving diffeomorphisms which are not twist maps. Several properties analogous to those of classical regions of instability are…

We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…

The inner moons of Jupiter and Saturn migrate outwards due to tidal energy dissipation within the planets, the details of which remain poorly understood. We demonstrate that resonance locking between moons and internal oscillation modes of…

Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…

For Hamiltonian systems with degeneracy of any higher order, we study the persistence of resonant invariant tori, which as some lower-dimensional invariant tori might be elliptic, hyperbolic or of mixed types. Hence we prove a quasiperiodic…

Wave resonance is the fundamental mechanism of non-linear instabilities of fluid flows, and affects the long-time evolution of fluid motions and other physical problems described by non-linear differential equations. Some significant…