BTZ dynamics and chaos

Nonlinear Dynamics and Chaos

Throughout much of ecology’s history, most ecologists have believed that ecological systems tend towards an equilibrium – a notion popularized as ‘the balance of nature’ – and that deviations from that equilibrium are caused by external perturbations. By assuming that systemswere close to equilibrium, ecologists coulddescribe them with linear models that were mathematically tractable. However, ...

Bulk and Boundary Dynamics in BTZ Black Holes

Recently, the AdS/CFT conjecture of Maldacena has been investigated in Lorentzian signature by Balasubramanian et. al. We extend this investigation to Lorentzian BTZ black hole spacetimes, and study the bulk and boundary behaviour of massive scalar fields both in the non-extremal and extremal case. Using the bulk-boundary correspondence, we also evaluate the two-point correlator of operators co...

Chaos, causation, and describing dynamics

Chaos without nonlinear dynamics.

A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. Th...

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos

A new computational technique based on the symbolic description utilizing kneading invariants is proposed, and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detects their organizing centers — codimension-two T-points and...