A computer-assisted proof of symbolic dynamics in Hyperion's inner rotation model

The rotation of Hyperion is often modelled by equations of motion of an ellipsoidal satellite. The model is expected to be chaotic for large range of parameters. The paper contains a rigorous computer-assisted proof of the existence of symbolic dynamics in its dynamics by the use of CAPD C++ library.Comment: 14 pages, 11 figure

On integrability of the Szekeres system. I

The Szekeres system is a four-dimensional system of first-order ordinary differential equations with nonlinear but polynomial (quadratic) right-hand side. It can be derived as a special case of the Einstein equations, related to inhomogeneous and nonsymmetrical evolving spacetime. The paper shows how to solve it and find its three global independent first integrals via Darboux polynomials and Jacobi’s last multiplier method. Thus the Szekeres system is completely integrable. Its two-dimensional subsystem is also investigated: we present its solutions explicitly and discuss its behaviour at infinity

On the cohomology of an isolating block and its invariant part

We give a sufficient condition for the existence of an isolating block $B$ for an isolated invariant set $S$ such that the inclusion induced map in cohomology $H^* (B)\to H^*(S)$ is an isomorphism. We discuss the Easton's result concerning the special case of flows on a $3$-manifold. We prove that if $S$ is an isolated invariant set for a flow on a $3$-manifold and $S$ is of finite type, then each isolating neighbourhood of $S$ contains an isolating block $B$ such that $B$ and $B^-$ are manifolds with boundary and the inclusion induced map in cohomology is an isomorphism