Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - Part II

We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem (PCR3BP) corresponding to the Sun-Jupiter-Oterma system possesses an infinite number of symmetric periodic orbits and homoclinic orbits to the Lyapunov orbits. Moreover, we show the existence of symbolic dynamics on six symbols for PCR3BP and the possibility of resonance transitions of the comet. This extends earlier results by Wilczak and Zgliczynski - Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - A Computer Assisted Proof, Commun. Math. Phys. 234, 37-75 (2003).Comment: 18 pages, 5 figure

Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - A Computer Assisted Proof

The restricted circular three-body problem is considered for the following parameter values $C=3.03$, $\mu=0.0009537$ - the values for {\em Oterma} comet in the Sun-Jupiter system. We present a computer assisted proof of an existence of homo- and heteroclinic cycle between two Lyapunov orbits and an existence of symbolic dynamics on four symbols built on this cycle.Comment: 40 pages, 11 figure

Differences in reef fish assemblages between populated and remote reefs spanning multiple archipelagos across the central and western Pacific

Comparable information on the status of natural resources across large geographic and human impact scales provides invaluable context to ecosystem-based management and insights into processes driving differences among areas. Data on fish assemblages at 39 US flag coral reef-areas distributed across the Pacific are presented. Total reef fish biomass varied by more than an order of magnitude: lowest at densely-populated islands and highest on reefs distant from human populations. Remote reefs (<50 people within 100 km) averaged ~4 times the biomass of “all fishes” and 15 times the biomass of piscivores compared to reefs near populated areas. Greatest within-archipelagic differences were found in Hawaiian and Mariana Archipelagos, where differences were consistent with, but likely not exclusively driven by, higher fishing pressure around populated areas. Results highlight the importance of the extremely remote reefs now contained within the system of Pacific Marine National Monuments as ecological reference areas

Lagrangian Reachabililty

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201

Depth refuge and the impacts of SCUBA spearfishing on coral reef fishes

In recent decades, spearfishing with SCUBA has emerged as an efficient method for targeting reef fish in deeper waters. However, deeper waters are increasingly recognised as a potential source of refuge that may help sustain fishery resources. We used a combination of historical catch data over a 20-year time period and fishery-independent surveys to investigate the effects of SCUBA spearfishing on coral reef fish populations in the southern Mariana Islands. Two jurisdictions were studied; Guam, where SCUBA spearfishing is practiced, and the nearby Commonwealth of Northern Mariana Islands (CNMI), where SCUBA spearfishing has been banned since 2003. Fishery-independent data were collected using baited remote underwater stereo-video systems (stereo-BRUVs) stratified by depth, marine protected area status and jurisdiction. Herbivores (primary consumers) dominated spearfishing catches, with parrotfish (scarines) and surgeonfish/unicornfish (acanthurids) the main groups harvested. However, the large, endangered humphead wrasse (Cheilinus undulatus) was the main species by weight landed by SCUBA spearfishers. SCUBA spearfishing was associated with declining size of scarines over time and catches shifting from a dominance of large parrotfishes to a mixed assemblage with increasing proportions of acanthurids. Comparisons between Guam and the nearby CNMI revealed differences in the assemblage of fished species and also greater size of scarines and acanthurids in deep water where SCUBA fishing is banned. These results suggest that SCUBA spearfishing impacts reef fish populations and that the restriction of this fishing method will ensure refuge for fish populations in deeper waters. We recommend a ban on SCUBA spearfishing to preserve or aid the recovery of large, functionally important coral reef species and to improve the sustainability of coral reef fisheries

Symbolic Dynamics for the Henon-Heiles Hamiltonian on the Critical Level

We present a computer assisted proof of the existence of a rich symbolic dynamic structure for the HenonHeiles Hamiltonian system at the critical energy E=1/6

Symbolic Dynamics for the Henon-Heiles Hamiltonian on the Critical Level

We present a computer assisted proof of the existence of a rich symbolic dynamic structure for the HenonHeiles Hamiltonian system at the critical energy E=1/6