Related papers: Basin structure in the two-dimensional dissipative…
Generalized multibaker maps are introduced to model dissipative systems which are spatially extended only in certain directions and escape of particles is allowed in other ones. Effects of nonlinearity are investigated by varying a control…
The mode-locking regions of a dynamical system are the subsets of the parameter space of the system within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a curious chain…
The structure and evolution of gas flows within the cavity of a circumbinary disk (CBD) surrounding the stellar components in eccentric binaries are examined via two-dimensional hydrodynamical simulations. The degree to which gas fills the…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
In this paper we study the Cauchy problem for doubly dissipative elastic waves in two space dimensions, where the damping terms consist of two different friction or structural damping. We derive energy estimates and diffusion phenomena with…
Sandpiles have become paradigmatic systems for granular flow studies in statistical physics. New directions of investigations are discussed here. Rather than varying the nature of the pile (sand, salt, rice,..) we have investigated changes…
We study the dynamics of inertial particles in two dimensional incompressible flows. The Maxey-Riley equation describing the motion of inertial particles is used to construct a four dimensional dissipative bailout embedding map. This map…
The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a…
We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible maps unfolding generally the…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
We define fractal continuations and the fast basin of the IFS and investigate which properties they inherit from the attractor. Some illustrated examples are provided.
The process of forming a circumbinary planet is thought to be intimately related to the structure of the nascent circumbinary disc. It has been shown that the structure of a circumbinary disc depends strongly on 3-dimensional effects and on…
The aim of this work is to review and also explore even further the escape properties of orbits in a dynamical system of a two-dimensional perturbed harmonic oscillator, which is a characteristic example of open Hamiltonian systems. In…
We present a new model for two phase Darcy flows in fractured media, in which fractures are modelled as submanifolds of codimension one with respect to the surrounding domain (matrix). Fractures can act as drains or as barriers, since…
We present general design principles for engineering and discovering periodic systems with flat bands. Our paradigm exploits spin-orbit assisted orbital frustration on a lattice to produce band structures that contain multiplets of narrowly…
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the…
Here we show a complete band gap in acoustic propagation in water with regularly placed air-cylinders. Also for the first time, we report that in the gap, all cylinders oscillate in phase but exactly out of the phase of a wave source…
Consider a quadratic rational self-map of the Riemann sphere such that one critical point is periodic of period 2, and the other critical point lies on the boundary of its immediate basin of attraction. We will give explicit topological…
The nonlinear climbing sine map is a nonhyperbolic dynamical system exhibiting both normal and anomalous diffusion under variation of a control parameter. We show that on a suitable coarse scale this map generates an oscillating…