Related papers: A Dichotomy between Discrete and Continuous Spectr…

We consider substitutions on compact alphabets and provide sufficient conditions for the diffraction to be pure point, absolutely continuous and singular continuous. This allows one to construct examples for which the Koopman operator on…

We consider the local kinematics at fluid interfaces in two-phase flows within the sharp interface framework. In the considered case with phase change and slip at the interface, the governing velocity field is discontinuous at the phase…

We provide new bounds on a flux integral over the portion of the boundary of one regular domain contained inside a second regular domain, based on properties of the second domain rather than the first one. This bound is amenable to…

In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This enables us to answer positively a question of Bowen and…

For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a…

We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…

The work concerns the spectral, entropy and bifurcation analysis of the dynamics of a reverse-flow system. The existence of chaotic oscillations was demonstrated in a wide range of changes in the parameters of the model. The model of such a…

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…

Consider an arbitrary closed, countably $n$-rectifiable set in a strictly convex $(n+1)$-dimensional domain, and suppose that the set has finite $n$-dimensional Hausdorff measure and the complement is not connected. Starting from this given…

While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. In this paper, we show that flows can in fact be extended to…

We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we…

We define functionals generalising the Seiberg-Witten functional on closed $spin^c$ manifolds, involving higher order derivatives of the curvature form and spinor field. We then consider their associated gradient flows and, using a gauge…

Dynamics of a classical particle in a one-dimensional, randomly driven potential is analysed both analytically and numerically. The potential considered here is composed of two identical spatially-periodic saw-tooth-like components, one of…

We prove a variant of the Chance-McDuff conjecture for pseudo-rotations: under certain additional conditions, a closed symplectic manifold which admits a Hamiltonian pseudo-rotation must have deformed quantum product and, in particular,…

Fluid mixing usually involves the interplay between advection and diffusion, which together cause any initial distribution of passive scalar to homogenize and ultimately reach a uniform state. However, this scenario only holds when the…

Low angular momentum accretion flows very often have centrifugal pressure supported standing shock waves which can accelerate flow particles. The accelerated particles in turn emit synchrotron radiation in presence of magnetic fields.…

Flow type suspension and homotopy suspension agree for attractor-repellor homotopy data.The connection maps associated in Conley index theory to an attractor-repellor decomposition with respect to the direct flow and its inverse are…

We use spectral flow to present a new proof of Levinson's theorem for Schr\"{o}dinger operators on $\mathbb{R}^n$ with smooth compactly supported potential. Our proof is valid in all dimensions and in the presence of resonances. The…

We derive slow-roll conditions for a scalar field which is non-minimally coupled with gravity in a consistent manner and express spectral indices of scalar/tensor perturbations in terms of the slow-roll parameters. The conformal invariance…

We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to periodic pulsatile drives. The strange…