All possible chaotic dynamics can be approximated in three dimensions

All possible chaotic dynamics can be approximated in three dimensions

It is known that neither onenor two-dimensional ordinary differential equations can exhibit chaotic phenomena, while such behaviour is possible in threedimensional systems. Here it is shown that the solutions of any dissipative equation can be approximated arbitrarily closely by the trajectories of an appropriate threedimensional system. This class includes the Navier-Stokes equations, showing ...

Evolutionary Dynamics Can be Chaotic: a First Example

We present in this paper the first example of chaotic evolutionary dynamics in biology. We consider a Lotka-Volterra tritrophic food chain composed of a resource, its consumer, and a predator species, each characterized by a single adaptive phenotypic trait, and we show that for suitable modeling and parameter choices the evolutionary trajectories approach a strange attractor in the three-dimen...

What Can Be Approximated by Polynomials with Integer Coefficients

Can billiard eigenstates be approximated by superpositions of plane waves ?

The plane wave decomposition method (PWDM) is one of the most popular strategies for numerical solution of the quantum billiard problem. The method is based on the assumption that each eigenstate in a billiard can be approximated by a superposition of plane waves at a given energy. By the classical results on the theory of differential operators this can indeed be justified for billiards in con...

What can be seen in three dimensions with an uncalibrated stereo rig

1 I n t r o d u c t i o n The problem we address in this paper is that of a machine vision system with two cameras, sometimes called a stereo rig, to which no thro~-dimensional metric information has been made available. The only information at hand is contained in the two images. We assume that this machine vision system is capable, by comparing these two images, of establishing correspondence...