Related papers: Structure and evolution of strange attractors in n…
We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…
Chaotic properties of symmetrical two-dimensional stadium-like billiards with elliptical arcs are studied numerically and analytically. For the two-parameter truncated elliptical billiard the existence and linear stability of several…
Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov…
Based on both qualitative method and numerical tests for a series of particular cases in the parameter region, a=1, 0<b <1, it is shown that the three-dimensional system (2) may have a series of interesting phenomena on the non-trivial…
We investigate aspects of low-magnetic-Reynolds-number flow between two parallel, perfectly insulating walls, in the presence of an imposed magnetic field parallel to the bounding walls. We find a functional basis to describe the flow, well…
We examine the spectral properties of three-dimensional quantum billiards with a single pointlike scatterer inside. It is found that the spectrum shows chaotic (random-matrix-like) characteristics when the inverse of the formal strength…
Dynamical focusing of ensembles of neutral particles in energy and configuration space has been demonstrated recently [C. Petri et al. 2010, Phys. Rev. E (R) {\bf 82}, 035204] using time-dependent elliptical billiards. The interplay of…
The form factor $K(\tau)$ is calculated analytically to the order $\tau^3$ as well as numerically for a rectangular billiard perturbed by a $\delta$-like scatterer with an angle independent diffraction constant, $D$. The cases where the…
Non-conformal attractor behavior is studied by solving non-conformal second order viscous hydrodynamics with respect to boost-invariant plasmas. Numerical solutions of the relative decay rate of the enthalpy density, the inverse shear and…
We study a free interface problem related to combustion of condensed matter and some non-equilibrium exothermal phase transitions. In spite of a variety of non-trivial dynamical scenarios exhibited by the model the solutions are uniformly…
Parametric modulation in nonlinear dynamical systems can give rise to attractors on which the dynamics is aperiodic and nonchaotic, namely with largest Lyapunov exponent being nonpositive. We describe a procedure for creating such…
We study the attractor equations for a quantum corrected prepotential F=t^3+i\lambda, with \lambda \in R,which is the only correction which preserves the axion shift symmetry and modifies the geometry. By performing computations in the…
We investigate statistical properties of several classes of periodic billiard models which are diffusive. An introductory chapter gives motivation, and then a review of statistical properties of dynamical systems is given in chapter 2. In…
In this paper, we construct an iterated function system on the line consisting of two bi-Lipschitz contractions whose attractor has distinct lower, Hausdorff, lower box, upper box, and Assouad dimensions, thereby providing negative answers…
We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…
Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously in some parameter regimes. Here we…
Deterministic and time-reversible nonequilibrium molecular dynamics simulations typically generate "fractal" [ fractional-dimensional ] phase-space distributions. Because these distributions and their time-reversed twins have zero phase…
Considering random noise in finite dimensional parameterized families of diffeomorphisms of a compact finite dimensional boundaryless manifold M, we show the existence of time averages for almost every orbit of each point of M, imposing…
We study outer billiards with contraction outside regular polygons. For regular $n$-gons with $n = 3, 4, 5, 6, 8$, and $12$, we show that as the contraction rate approaches $1$, dynamics of the system converges, in a certain sense, to that…
We consider statistical attractors of locally typical dynamical systems and their "e-invisible" subsets: parts of the attractors whose neighborhoods are visited by orbits with an average frequency of less than e << 1. For extraordinarily…