AGarsia number is an algebraic integer of norm ±2 such that all of the roots of its minimal polynomial are strictly greater than 1 in absolute value. Little is known about the structure of the set of Garsia numbers. The only known limit point of positive real Garsia numbers was 1 (given, for example, by the set of Garsia numbers 21/n). Despite this, there was no known interval of [1,2] where th...

We consider both hyperbolic sets and partially hyperbolic sets attracting a set of points with positive volume in a Riemannian manifold. We obtain several results on the topological structure of such sets for diffeomorphisms whose differentiability is bigger than one. We show in particular that there are no partially hyperbolic horseshoes with positive volume for such diffeomorphisms. We also g...

We prove that the property to be limit aperiodic is preserved by the standard construction with groups like extension, HNN extension and free product. We also construct a non-limit aperiodic G-space.

Reversibility is a widely accepted principle in physics, according to which, the microscopic laws governing the dynamics of the physical nature can hypothetically be reversed to let the system run backward in time. Reversible cellular automata (CA) have been extensively studied as convenient tools for modeling physical systems, whenever capturing the microscopic reversibility is desirable (see ...

The A–polynomial of a manifold whose boundary consists of a single torus is generalised to an eigenvalue variety of a manifold whose boundary consists of a finite number of tori, and the set of strongly detected boundary curves is determined by Bergman’s logarithmic limit set, which describes the exponential behaviour of the eigenvalue variety at infinity. This enables one to read off the detec...

A coamoeba is the image of a subvariety of a complex torus under the argument map to the real torus. We describe the structure of the boundary of the coamoeba of a variety, which we relate to its logarithmic limit set. Detailed examples of lines in three-dimensional space illustrate and motivate these results.