In this paper we describe the Garnier systems as isomonodromic deformation equations of a linear system with a simple pole at 0 and a Poincaré rank two singularity at infinity. We discuss the extension of Okamoto’s birational canonical transformations to the Garnier systems in more than one variable and to the Schlesinger systems.

Stable chaos refers to the long irregular transients, with a negative largest Lyapunov exponent, which is usually observed in certain high-dimensional dynamical systems. The mechanism underlying this phenomenon has not been well studied so far. In this paper, we investigate the dynamical formation of stable irregular transients in coupled discontinuous map systems. Interestingly, it is found th...

Irregular applications are characterized by highly irregular and ne-grained data referencing patterns. When there is poor locality between the ne-grained data, serious false sharing can occur which has largely contributed to poor performance of irregular applications on page-based software distributed shared memory (DSM) systems. Partitioning data in irregular applications to improve data local...

This paper examines the limits of performance in systems with periodic irregular sampling rate when the actuation is not necessarily synchronized with the sampling. For such a system, three sampling and actuation schemes are considered: when the sampling and control rate are both regular, when they are both irregular, and when the sampling rate is irregular while the control rate is regular. To...

We systematically investigate examples of non-hyperbolic dynamical systems having irregular sets full topological entropy and Hausdorff dimension. The include some partially hyperbolic geometric Lorenz flows. also pose interesting questions for future research.

This paper presents PIT, a library for the parallelization of irregular problems on distributed memory architectures. All the strategies underlying the definition of the library can be expressed in terms of operations on a PITree, a parallel version of the tree data structure oriented to irregular problems. We consider the application of PIT to two well known irregular problems: adaptive multig...