Related papers: Moser's twist theorem revisited
We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family…
The $Z_2$ invariant for filled bands in the ground states of systems with time reversal invariance characterizes the number of stable pairs of edge states. Here we study the $Z_2 $ invariant using band touching methods discussed in a recent…
Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth function c(x,y). If the source density f^+(x) is bounded…
In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving homeomorphisms of the $n$-ball is simple for $n \ge 3$, asked if the same statement holds in dimension $2$. We show that the group of compactly…
We develop a new method to estimate the area, and more generally the intrinsic volumes, of a compact subset $X$ of $\mathbb{R}^d$ from a set $Y$ that is close in the Hausdorff distance. This estimator enjoys a linear rate of convergence as…
We use the embedding of Einstein gravity with cosmological constant into conformal gravity as a basis for using the twistor action for conformal gravity to obtain MHV scattering amplitudes not just for conformal gravity, but also for…
The twist interval of a twist map on the annulus $A=\mathbb{T}\times [0,1]$ has nonempty interior if $f$ preserves the area, but could be degenerate for general twist maps. In this note, we show that if a twist map $f$ is non-wandering,…
We show that the main theorem of Morse theory holds for a large class of functions on singular spaces. The function must satisfy certain conditions extending the usual requirements on a manifold that Condition C holds and the gradient flow…
We prove twisted homological stability with polynomial coefficients for automorphism groups of free nilpotent groups of any given class. These groups interpolate between two extremes for which homological stability was known before, the…
We study contraction conditions for an iterated function system of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space,…
Symmetries and their anomalies are powerful tools to understand quantum matter. In this work, for quantum spin chains, we define twisted locality-preserving automorphisms and their Gross-Nesme-Vogts-Werner indices, which provide a unified…
A discontinuous area-preserving mapping derived from a sinusoidally-forced impacting system is studied. This system, the elastic impact oscillator, is very closely related to the accelerator models of particle physics such as the Fermi map.…
Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moir\'e twisted bilayers with time-reversal symmetry and…
We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…
We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic…
The Tayler instability of an azimuthal magnetic field with one or two ``rings'' along the radius is studied for an axially unbounded Taylor-Couette flow. The rotation law of the conducting fluid is a quasi-Keplerian one. Without rotation…
The stability of an initially one-dimensional electron hole to perturbations varying sinusoidally transverse to its trapping direction is analysed in detail. It is shown that the expected low-frequency eigenmode of the linearized…
In this paper, we establish the existence of periodic orbits of a twisted geodesic flow on all low energy levels and in all dimensions whenever the magnetic field form is symplectic and spherically rational. This is a consequence of a more…
We prove a very general Weyl-type law for Periodic Floer Homology, estimating the action of twisted Periodic Floer Homology classes over essentially any coefficient ring in terms of the grading and the degree, and recovering the Calabi…
We use Heegaard Floer homology with twisted coefficients to define numerical invariants for arbitrary closed 3-manifolds equipped torsion spin$^c$ structures, generalising the correction terms (or $d$--invariants) defined by Ozsv\'ath and…