Related papers: Pentagonal Domain Exchange
The internal structure of domains smaller than the characteristic size in domain coarsening dynamics of $Z_2$ symmetry breaking is evaluated theoretically for different phase ordering systems in two dimensions. In the previous works on…
Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we…
We address the problems in applying cycle expansions to bound chaotic systems, caused by e.g. intermittency and incompleteness of the symbolic dynamics. We discuss zeta functions associated with weighted evolution operators and in…
The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
In this paper we study in detail, both analytically and numerically, the dynamical properties of the triangle map, a piecewise parabolic automorphism of the two-dimensional torus, for different values of the two independent parameters…
Periodically driven dynamics of a particle moving in the field Coulomb plus confining potential is treated for one and three dimensional cases. Critical value of the external field strength at which chaotization will occur is evaluated…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
We elucidate the pivotal role of the bandstructure's orbital content in deciding the type of commensurate magnetic order stabilized within the itinerant scenario of iron-pnictides. Recent experimental findings in the tetragonal magnetic…
Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple, paradigmatic case of equal-strength, all-to-all sine-coupling of phase oscillators subject to a…
Quantum substitutions of Pisot type (and their quantum topological entropy) are introduced. Their utility as algorithms for optimal spacing is analyzed.
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic…
Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems, they are often treated rather superficially, if at all, in…
We report the first definitive experimental observation of periodic orbits (POs) in the spectral properties of an elastodynamic system. The Fourier transform of the density of flexural modes show peaks that correspond to stable and unstable…
We establish conditions for the existence of a family of piecewise linear invariant curves in a two-parameter family of piecewise isometries on the upper half-plane known as Translated Cone Exchange Transformations. We show that these…
A parametrized spin model was recently introduced and intended for one-dimensional ferromagnets with a deformable Zeeman energy. This model is revisited and given more realistic interpretation in terms of a model for ferromagnetic systems…
Each of the local isometry groups arising in 3d gravity can be viewed as the group of unit (split) quaternions over a ring which depends on the cosmological constant. In this paper we explain and prove this statement, and use it as a…
The nonreciprocal wave propagation in PT-symmetric periodic stack of binary dielectric layers characterised by balances loss and gain is analysed. The main mechanisms and resonant properties of the scattered plane waves are illustrated by…
We study an intrinsic distribution, called polar, on the space of $l$-dimensional integral elements of the higher order contact structure on jet spaces. The main result establishes that this exterior differential system is the prolongation…