Chaotic dynamics can be quite heterogeneous in the sense that some regions are unstable more directions than other regions. When trajectories wander between these regions, is complicated. We say a chaotic invariant set when arbitrarily close to each point of there different periodic points with numbers dimensions. call such chaos (or hetero-chaos), While we believe it common for physical system...

We present a technique for computing piecewise linear approximations of geodesics on point set surfaces by minimizing an energy function defined for piecewise linear path. The function considers path length, closeness to the surface for the nodes of the piecewise linear path and for the intermediate line segments. Our method is robust with respect to noise and outliers. In order to avoid local ...

We give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles. For the piecewise linear one, we mainly analyze the conforming case, but the present results also appear to be available for the non-conforming case. We obtain explicit relations for the upper bounds of the constants, and analyze dependence of su...