The evolution of n–dimensional graphs under a weighted curvature flow is approximated by linear finite elements. We obtain optimal error bounds for the normals and the normal velocities of the surfaces in natural norms. Furthermore we prove a global existence result for the continuous problem and present some examples of computed surfaces.

Schweizer and Smítal introduced the distributional chaos for continuous maps of the interval in B. Schweizer, J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Amer. Math. Soc. 344 (1994), 737–854. In this paper, we discuss the distributional chaos DC1–DC3 for flows on compact metric spaces. We prove that both the distributional chaos DC1 and DC2 of a flow are equivalent to the time-1 maps and so some properties of DC1 and DC2 for discrete systems...

Let $𝕏=\{z\in ℂ:z^n\in [0,1]\}$, $n\in \mathbb{N}$, and let $f:𝕏\to 𝕏$ be a continuous map having the branching point fixed. We prove that $f$ is distributionally chaotic iff the topological entropy of $f$ is positive.