An existence of simple choreographies for N-body problem - a computer assisted proof

We consider a question of finding a periodic solution for the planar Newtonian N-body problem with equal masses, where each body is travelling along the same closed path. We provide a computer assisted proof for the following facts: local uniqueness and convexity of Chenciner and Montgomery Eight, an existence (and local uniqueness) for Gerver's SuperEight for 4-bodies and a doubly symmetric linear chain for 6-bodies.Comment: 19 pages, 9 figure

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

Cone Conditions and Covering Relations for Topologically Normally Hyperbolic Invariant Manifolds

We present a topological proof of the existence of invariant manifolds for maps with normally hyperbolic-like properties. The proof is conducted in the phase space of the system. In our approach we do not require that the map is a perturbation of some other map for which we already have an invariant manifold. We provide conditions which imply the existence of the manifold within an investigated region of the phase space. The required assumptions are formulated in a way which allows for rigorous computer assisted verification. We apply our method to obtain an invariant manifold within an explicit range of parameters for the rotating H\'enon map

Transition Tori in the Planar Restricted Elliptic Three Body Problem

We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2, a Cantor set of Lyapounov orbits survives the perturbation. The orbits are perturbed to quasi-periodic invariant tori. We show that for a certain family of masses of the primaries, for such tori we have transversal intersections of stable and unstable manifolds, which lead to chaotic dynamics involving diffusion over a short range of energy levels. Some parts of our argument are nonrigorous, but are strongly backed by numerical computations

Thermal Profile Of A Reciprocating Compressor Using Low GWP Refrigerants

To contribute to the global effort to phase down highly polluting HFC refrigerants, refrigeration industry is dedicating significant resources in evaluation process of alternative refrigerants. In the light commercial refrigeration segment the most difficulties were found to replace R404A refrigerant. Embraco, being one of major compressors manufacturers, took part in AHRI AREP program with performances evaluation on several refrigerant alternatives with GWP below 150, limit that is widely used as a threshold in regional and local legislations in the years to come. Except natural refrigerants like hydrocarbons and CO2, new chemical blends, classified in A2L safety class, were developed with GWP \u3c 150 to meet criteria of regional regulation in different parts of the world. This paper shows summary of evaluation of a hermetic reciprocating compressor based on its thermal profile when using an A2L blend. It is then compared with R404A and R290 profiles in order to understand limitations when using an A2L chemical blend in the product which originally have been designed for R404A operation

Central configurations in spatial n-body problem for n = 5, 6 with equal masses

We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for n = 5 and 6, with equal masses. For each central configuration we give a full list of its euclidean symmetries. For all masses sufficiently close to the equal masses case we give an exact count of configurations in the planar case for n = 4, 5, 6, 7 and in the spatial case for n = 4, 5, 6.Comment: The program with a manual and reports from program runs can be downloaded at http://ww2.ii.uj.edu.pl/~zgliczyn/papers/publ.ht