Related papers: Some constructions of Weinstein manifolds with cha…
Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify…
We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet that is periodically kicked with a delta function…
Let $X$ be a Stein manifold of dimension $n\geq 2$ satisfying the volume density property with respect to an exact holomorphic volume form. For example, $X$ could be $\mathbb{C}^n$, any connected linear algebraic group that is not…
We study the resonant tunneling effect in a many-body Wannier-Stark system, realized by ultracold bosonic atoms in an optical lattice subjected to an external Stark force. The properties of the many-body system are effectively described in…
One generally expects that the techniques of arboreal singularities and gluing of local differential graded categories will result in a useful global invariant for all Weinstein manifolds. In this paper we construct explicit models for the…
Many dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are…
In this paper we clarify an issue in the knot surgery construction of Fintushel and Stern. Using knot surgery, they construct an infinite number of smooth structures on 4-manifolds satisfying certain conditions, but they do not explicitly…
A geodesic orbit manifold is a complete Riemannian manifold all of whose geodesics are orbits of one-parameter groups of isometries. We give both a geometric and an algebraic characterization of geodesic orbit manifolds that are…
In this paper, we derive the second variation formula of pseudoharmonic maps into any pseudo-Hermitian manifolds. When the target manifold is an isometric embedded CR manifold in complex Euclidean space or a pseudo-Hermitian immersed…
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper. Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the…
We describe the statistics of chaotic wavefunctions near periodic orbits using a basis of states which optimise the effect of scarring. These states reflect the underlying structure of stable and unstable manifolds in phase space and…
The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The…
The Weinstein conjecture, as the general existence problem for periodic orbits of Hamiltonian or Reeb flows, has been among the central questions in symplectic topology for over two decades and its investigation has led to understanding of…
The chaotic phase of the tilted Bose-Hubbard model is identified as a function of energy, tilt strength and particle interaction, from the eigenstate structure and the statistical features of the energy spectrum. Our analysis reveals that…
We propose a novel framework for analyzing the geometric structure of horseshoes arising in three- and four-dimensional H\'enon-type maps by introducing paperfolding structures as geometric templates. These structures capture the folding…
The nonlinear dynamics of a recently derived generalized Lorenz model (Macek and Strumik, Phys. Rev. E 82, 027301, 2010) of magnetoconvection is studied. A bifurcation diagram is constructed as a function of the Rayleigh number where…
Chaotic systems, presenting complex and non-reproducible dynamics, may be found in nature from the interaction between planets to the evolution of the weather, but can also be tailored using current technologies for advanced signal…
Inspired by Katok's examples of Finsler metrics with a small number of closed geodesics, we present two results on Reeb flows with finitely many periodic orbits. The first result is concerned with a contact-geometric description of magnetic…
We work out the construction of a Stein manifold from a commutative Arens-Michael algebra, under assumptions that are mild enough for the process to be useful in practice. Then, we do the passage to arbitrary complex manifolds by proposing…