The basic concept of fractals and multifractals are introduced for pedagogical purposes, and
the present status is reviewed. The emphasis is put on illustrative examples with simple …

Fractals arise from a variety of sources and have been observed in nature and on computer
screens. One of the exceptional characteristics of fractals is that they can be described by a …

In this paper, two issues are addressed:(1) the applicability of the delay-coordinate
embedding method to transient chaotic time series analysis, and (2) the Hilbert transform …

This book is a monograph on chaos in dissipative systems written for those working in the
physical sciences. Emphasis is on symbolic description of the dynamics and various …

Based on chaos theory two very important points are clear:(I) random looking aperiodic
behavior may be the product of determinism, and (2) nonlinear problems should be treated …

The probability measure generated by typical chaotic orbits of a dynamical system can have
an arbitrarily fine-scaled interwoven structure of points with different singularity scalings …

Human's observation and measurement of natural phenomena are always carried out with
finite precision. This precision improves with the advance of science and technology, but it …

We use the set of all periodic points of Hénon-type mappings to develop a theory of the
topological and metric properties of their attractors. The topology of a Hénon-type attractor is …

I use a thermodynamic formalism to study the spectrum f (α) which characterises the large
fluctuations of pointwise dimension in a Gibbs state supported on a hyperbolic cookie-cutter …

Transient phenomena have always played an important role in various fields of Science. In
the last two decades we also learned that chaotic processes are common ubiquitous in the …