Floyd gave an example of a minimal dynamical system which was extension odometer and the fibres associated factor map were either singletons or intervals. Gjerde Johansen showed that could be replaced by any Cantor system. Here, we show further intervals can generalized to cubes arbitrary dimension attractors certain iterated function systems. We discuss applications.

We investigate non-homogeneous Hamiltonian operators composed of a first order Dubrovin–Novikov operator and an ultralocal one. The study such turns out to be fundamental for the inverted system equations associated with class scalar equations. Often, involved are degenerate in term. For this reason, complete classification leading coefficient systems two three components is presented.

The improved description of the planets’ interior is provided. We examine modified gravity effects on Earth-like planets composed iron core and silicate mantle. confirm that mass–radius relations as well density profiles differ with respect to commonly adopted Newtonian models.

The wave equation ?tt?c2?xu(x,t)=e?tf(x,t) in the cone {(x,t):?x??t,x?Rd,t?R+} is shown to have a unique solution if u and its partial derivatives x are L2(e?t) on cone, can be explicit given Fourier series of orthogonal polynomials cone. This provides particular for boundary value problems non-homogeneous which combined with homogeneous obtain full solution.

We investigate the motion of contact surface centroid for contractile bodies on substrates with a viscous friction law and when inertial forces are negligible. deduce set sufficient conditions that ensure remains still. In linear analysis, coefficient is required to be homogeneous constant. non-linear additional necessary: (i) material must incompressible, (ii) points in cannot vary, (iii) flat...