The self-rotation number, as defined by Peckham, is the rotation rate of the image of a point about itself. Here we use the notion of “turning angle” to give a simplified algorithm to compute the selfrotation number for maps that “avoid an angle.” We show that the orientation preserving Hénon map does avoid an angle. Moreover, the self-rotation number for orbits of the Hénon map can be computed...

In a recent paper, T. Kohonen and P. Somervuo have shown that self-organizing maps (SOMs) are not restricted to numerical data. They can also be defined for symbol strings, provided that one defines an average function for strings and that the adaptation process is performed off-line (batch). In this paper, we present two different methods for computing averages of strings, as well as an on-lin...

The Mullineux involution is a relevant map that appears in the study of modular representations symmetric group and alternating group. fixed points this are certain partitions particular interest. It known cardinality set these self-Mullineux equal to distinguished subset self-conjugate partitions. In work, we give an explicit bijection between two families terms symbol.

We prove an index theorem for boundary value problems in Boutet de Monvel’s calculus on a compact manifold X with boundary. The basic tool is the tangent semigroupoid T −X generalizing the tangent groupoid defined by Connes in the boundaryless case, and an associated continuous field C∗ r (T −X) of C∗-algebras over [0, 1]. Its fiber in ~ = 0, C∗ r (T−X), can be identified with the symbol algebr...

Context-sensitive rewriting (CSR) is a restriction of rewriting which forbids reductions on selected arguments of functions. A replacement map discriminates, for each symbol of the signature, the argument positions on which replacements are allowed. If the replacement restrictions are less restrictive than those expressed by the so-called canon-ical replacement map, then CSR can be used for com...

Symbolic codes for rotational orbits and “islands-around-islands” are constructed for the quadratic, area-preserving Hénon map. The codes are based upon continuation from an anti-integrable limit or, alternatively, from the horseshoe. Given any sequence of rotation numbers we obtain symbolic sequences for the corresponding elliptic and hyperbolic rotational orbits. These are shown to be consist...