The dynamical systems on the classical fractals can naturally be obtained with help of their iterated function systems. In recent years, different ways have been developed to define self similar sets. this paper, we give composition functions by using expanding and folding mappings which generate Sierpinski Gasket via escape time algorithm. These also indicate fractal. We express code represent...

We study quantum vortex states consisting of a ring vortices with alternating sign, in homogeneous superfluid confined to circular domain. find an exact stationary solution the point model for neutral necklace. investigate stability necklace state within both point-vortex and Gross-Pitaevskii equation describing trapped atomic Bose-Einstein condensate at low temperature. The are found also be p...

This paper considers the problem of planning collision-free motion of three disks in the plane. One of the three disks, the robot, can autonomously translate in the plane, the other two move only when in contact with the robot. This represents the abstract formulation of a manipulation planning problem. Despite the simplicity of the formulation, the decidability of the problem had remained unpr...

Walking, as an important transportation mode, plays a large part in urban transportation systems. This mode is of great importance for planners and decision-makers because of its impact on environmental and health aspects of communities. However, this mode is so complex in nature that makes it difficult to study or model. On the other hand, chaos theory studies complex dynamical nonlinear syste...

Devaney defines a function to be chaotic if it satisfies three conditions: transitivity, having dense set of periodic points and sensitive dependence on initial conditions. Banks et al prove that if the function is continuous then the third conditioin is implied from the first two and therefore is redundant. However, if the function is not assumed to be continuous, then it is not known if the t...

In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to the question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that the boundary is a quasi-circle if it con...

Makienko's conjecture, a proposed addition to Sul-livan's dictionary, can be stated as follows: The Julia set of a rational function R : C ∞ → C ∞ has buried points if and only if no component of the Fatou set is completely invariant under the second iterate of R. We prove Makienko's conjecture for rational functions with Julia sets that are decomposable continua. This is a very broad collectio...

Abstract Entropy is a standard measure used to determine the uncertainty, randomness, or chaos of experimental outcomes and quite popular in statistical distribution theory. methods available literature quantify information random variable with exact numbers lacks dealing interval value data. An indeterminate state an experiment generally generates data form. The indeterminacy property interval...