How to detect Wada Basins

Weak dissipation drives and enhances Wada basins in three-dimensional chaotic scattering

Chaotic scattering in three dimensions has not received as much attention as in two dimensions so far. In this paper, we deal with a three-dimensional open Hamiltonian system whose Wada basin boundaries become non Wada when the critical energy value is surpassed in the absence of dissipation. In particular, we study here the dissipation effects on this topological change, which has no analogy in two dimensions. Hence, we find that non-Wada basins, expected in the absence of dissipation, transform themselves into partially Wada basins when a weak dissipation reduces the system energy below the …

Ascertaining when a basin is Wada: the merging method

Trying to imagine three regions separated by a unique boundary seems a difficult task. However, this is exactly what happens in many dynamical systems showing Wada basins. Here, we present a new perspective on the Wada property: A Wada boundary is the only one that remains unaltered under the action of merging the basins. This observation allows to develop a new method to test the Wada property, which is much faster than the previous ones. Furthermore, another major advantage of the merging method is that a detailed knowledge of the dynamical system is not required.

The saddle-straddle method to test for Wada basins

First conceived as a topological construction, Wada basins abound in dynamical systems. Basins of attraction showing the Wada property possess the particular feature that any small perturbation of an initial condition lying on the boundary can lead the system to any of its possible outcomes. The saddle-straddle method, described here, is a new method to identify the Wada property in a dynamical system based on the computation of its chaotic saddle in the fractalized phase space. It consists of finding the chaotic saddle embedded in the boundary between the basin of one attractor and the remain…

双曲裤子曲面上的 Wada 边界

Wada Boundaries on a Hyperbolic Pair of Pants

本文用数值动力系统方法研究开放双曲裤子曲面上测地线的逃逸行为，发现吸引盆边界具有 Wada 性质，并证明盆熵依赖于逃逸通道的开口角度。

鲁棒的瓦达边界与pp波时空中的熵标度

Robust Wada Boundaries and Entropy Scaling in pp-Wave Spacetimes

研究pp波时空中的测地线动力学，揭示瓦达性质在多项式次数变化下的鲁棒性，并通过计算盆地熵和边界盆地熵量化动态不确定性，发现熵随多项式次数增加而单调上升，证实边界具有分形特性。

Wada structures in a binary black hole system

A key goal of the Event Horizon Telescope is to observe the shadow cast by a black hole. Recent simulations have shown that binary black holes, the progenitors of gravitational waves, present shadows with fractal structure. Here we study the binary shadow structure using techniques from nonlinear dynamics, recognising shadows as exit basins of open Hamiltonian dynamical systems. We apply a recently developed numerical algorithm to demonstrate that parts of the Majumdar-Papapetrou binary black hole shadow exhibit the Wada property: any point of the boundary of one basin is also on the boundary …