Related papers: Unstable periodic orbits in a chaotic meandering j…
Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics, and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
Planetary debris is observed in the atmospheres of over 1,000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through…
The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
In this numerical study, recurrence quantification analysis of chaotic trajectories is explored to detect atypical dynamical behaviour in non-linear Hamiltonian systems. An ensemble of initial conditions is evolved up to a maximum iteration…
An analytic theory is developed for the density of states oscillations in quantum wells in a magnetic field which is tilted with respect to the barrier planes. The main oscillations are found to come from the simplest one or two-bounce…
Quasiperiodicity, a partially synchronous state that precedes the onset of forced synchronization in hydrodynamic systems, exhibits distinct geometrical patterns based on the specific route to lock-in. In this study, we explore these…
Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling…
We investigate the natural families of periodic orbits associated with the equilibrium configurations of the the planar restricted $1+n$ body problem for the case $2\leq n \leq 4$ equal mass satellites. Such periodic orbits can be used to…
In a recent Letter, Hunt and Ott argued that SHORT-period unstable periodic orbits (UPOs) would be the invariant sets associated with a chaotic attractor that are most likely to optimize the time average of some smooth scalar performance…
Astrophysical objects frequently exhibit some irregularities or complex behaviour in their light curves. We focus primarily on hot stars, where both radial and non-radial pulsations are observed. One of the primary research goals is to…
Apparent evolution of relativistic flows as traced by radio emission results from a combination of several factors related to propagation of relativistic blobs or shocks, velocity, density and pressure stratification of the underlying flow,…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
We investigate some qualitative aspects of the dynamics of the Euler equation on a rotating sphere that are relevant or stratospheric flows. Zonal flow dominates the dynamics of the stratosphere and for most known planetary stratospheres…
Periodic orbits for the classical $\phi^4$ theory on the one dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, fixed and free boundary conditions. Through the process, we…
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of…
Active flow control (AFC) methods for jet-type flows have been extensively explored since the 1970s. Spectacular examples demonstrating the AFC power and the beauty of fluid mechanics include bifurcating and blooming jets. Recent advances…
One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional…
Active nematics in two dimensions stir themselves efficiently through internally generated chaotic flows, largely driven by motile $+1/2$ disclinations. We investigate how this tendency toward chaotic fluid stirring can, counterintuitively,…