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In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
We consider synchrony patterns in coupled phase oscillator networks that correspond to invariant tori. For specific nongeneric coupling, these tori are equilibria relative to a continuous symmetry action. We analyze how the invariant tori…
We study the problem of conservation of maximal and lower-dimensional invariant tori for analytic convex quasi-integrable Hamiltonian systems. In the absence of perturbation the lower-dimensional tori are degenerate, in the sense that the…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
Recent works have reported on the collective behavior of multiphase systems under fractional flow. Such behavior has been linked to pressure and/or flux fluctuations under stationary flow conditions that occur over a broad range of…
We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a…
A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin-Kasteleyn random…
Classifying phases of local quantum systems is a general problem that includes special cases such as free fermions, commuting projectors, and others. An important distinction in this classification should be made between classifying…
Certain objects of conformal field theory, for example partition functions on the rectangle and the torus, and one-point functions on the torus, are either invariant or transform simply under the modular group, properties which should be…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
In many shear- and pressure-driven wall-bounded turbulent flows secondary motions spontaneously develop and their interaction with the main flow alters the overall large-scale features and transfer properties. Taylor-Couette flow, the fluid…
We consider a photonic lattice of nonlinear lossy resonators subjected to a coherent drive, where the system remembers its topological phase. Initially, the system is topologically trivial. After the application of an additional coherent…
Topological metamaterials exhibit unusual behaviors at their boundaries, such as unidirectional chiral waves, that are protected by a topological feature of their band structure. The ability to tune such a material through a topological…
Context. Active regions (ARs) appear in the solar atmosphere as a consequence of the emergence of magnetic flux tubes. The presence of elongated magnetic polarities in line-of-sight (LOS) magnetograms indicates the existence of twist in the…
It is well-known that the resonance phenomena can destroy the adiabatic invariance and cause chaos and mixing. In the present paper we show that the nonlinear wave-particle resonant interaction may cause the emergence of large-scale…
This paper mainly concerns the KAM persistence of the mapping $\mathscr{F}:\mathbb{T}^{n}\times E\rightarrow \mathbb{T}^{n}\times \mathbb{R}^{n}$ with intersection property, where $E\subset \mathbb{R}^{n}$ is a connected closed bounded…
In this paper, we study the behaviour of TF-isomorphisms, a natural generalisation of isomorphisms. TF-isomorphisms allow us to simplify the approach to seemingly unrelated problems. In particular, we mention the Neighbourhood…
Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterised by topological invariants. In energy-conserving…
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modeling to everyday life devices. The eigenfrequencies of conventional…
We give a classification of pairs (F, f) where F is a holomorphic foliation on a projective surface and f is a non-invertible dominant rational map preserving F. We prove that both the map and the foliation are integrable in a suitable…