Related papers: Resurvey of order and chaos in spinning compact bi…
Full general relativity requires that chaos indicators should be invariant in various spacetime coordinate systems for a given relativistic dynamical problem. On the basis of this point, we calculate the invariant Lyapunov exponents (LEs)…
We investigate the orbits of compact binary systems during the final inspiral period before coalescence by integrating numerically the second-order post-Newtonian equations of motion. We include spin-orbit and spin-spin coupling terms,…
Spinning compact binaries are shown to be chaotic in the Post-Newtonian expansion of the two body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the…
The leading-order spin-orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists of the Newtonian term, first post-Newtonian (1PN) and 2PN non-spin terms and 2PN spin-spin coupling.…
Levin (gr-qc/9910040) has shown that spinning compact binaries can be chaotic at second post-Newtonian order. However, when higher order dissipational effects are included, the dynamics will no longer be chaotic, though the evolution may…
The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general…
In a recent Letter, Schnittman and Rasio argue that they have ruled out chaos in compact binary systems since they find no positive Lyapunov exponents. In stark constrast, we find that the chaos discovered in the original paper under…
Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the…
We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic…
We consider classical two-dimensional Kepler system with spin-orbit coupling and show that at a sufficiently strong coupling it demonstrates a chaotic behavior. The chaos emerges since the spin-orbit coupling reduces the number of the…
Permanently deformed objects in binary systems can experience complex rotation evolution, arising from the extensively studied effect of spin-orbit coupling as well as more nuanced dynamics arising from spin-spin interactions. The ability…
Binary systems of rapidly spinning compact objects, such as black holes or neutron stars, are prime targets for gravitational wave astronomers. The dynamics of these systems can be very complicated due to spin-orbit and spin-spin couplings.…
We formally show that the conservative second post-Newtonian (PN) accurate dynamics of spinning compact binaries moving in eccentric orbits, when spin effects are restricted to the leading order spin-orbit interaction cannot be chaotic for…
We take into account the dynamics of a complete third post-Newtonian conservative Hamiltonian of two spinning black holes, where the orbital part arrives at the third post-Newtonian precision level and the spin-spin part with the spin-orbit…
We study the stability and chaos of three compact objects using post-Newtonian (PN) equations of motion derived from the Arnowitt-Deser-Misner-Hamiltonian formulation. We include terms up to 2.5 PN order in the orbital part and the leading…
We investigate the impact of internal spin on chaos in billiard systems. Extending the standard point-particle billiard by coupling translational and rotational degrees of freedom through a dimensionless spin parameter $\alpha = I/(mr^2)…
We derive a criterion for the onset of chaos in systems consisting of two massive, eccentric, coplanar planets. Given the planets' masses and separation, the criterion predicts the critical eccentricity above which chaos is triggered. Chaos…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
This study examines second-order dynamical systems incorporating Tikhonov regularization. It focuses on how nonlinearities induce bifurcations and chaotic dynamics. By using Lyapunov functions, bifurcation theory, and numerical simulations,…
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the…