Symbolic dynamics I. Finite dispersive billiards

Orbits in different dispersive billiard systems, e.g. the 3 disk system, are mapped into a topological well ordered symbol plane and it is showed that forbidden and allowed orbits are separated by a monotone pruning front. The pruning front can be approximated by a sequence of finite symbolic dynamics grammars.Comment: CYCLER Paper 93Jan00

Alternative method to find orbits in chaotic systems

We present here a new method which applies well ordered symbolic dynamics to find unstable periodic and non-periodic orbits in a chaotic system. The method is simple and efficient and has been successfully applied to a number of different systems such as the H\'enon map, disk billiards, stadium billiard, wedge billiard, diamagnetic Kepler problem, colinear Helium atom and systems with attracting potentials. The method seems to be better than earlier applied methods.Comment: 5 pages, uuencoded compressed tar PostScript fil

Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem

We describe the structure of bifurcations in the unbounded classical Diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the non-wandering set is described by a complete trinary symbolic dynamics for scaled energies larger then $\epsilon_c=0.328782\ldots$.Comment: 15 pages PostScript uuencoded with figure

Using ⁸⁷Sr/⁸⁶Sr Ratios to Date Fossil Methane Seep Deposits: Methodological Requirements and an Example from the Great Valley Group, California

Methane seep carbonates preserve information about the history of methane seepage and of the fauna inhabiting these ecosystems. For this information to be useful, a reliable determination of the carbonates’ stratigraphic ages is required, but this is not always available. Here we investigate the using strontium isotope stratigraphy to date fossil methane seep carbonates via detailed petrographic and geochemical investigation of the different carbonate phases in biostratigraphically well-dated seep carbonates of Paleozoic, Mesozoic, and Cenozoic age. The best results are obtained from banded, botryoidal rim cements from carbonate phases showing a weak or no cathodoluminescence signal, an oxygen isotope signature close to that of seawater, and the lowest Mn concentrations. We then applied the method to a presumably late Jurassic seep carbonate from the Great Valley Group in California. Strontium isotope ratios of the least diagenetically altered carbonate phases indicate a Tithonian (late Jurassic) age for this seep site, which is in conflict with a recent study that suggested the absence of Jurassic strata from the Great Valley Group