We prove geometric and scaling results for the real Fibonacci parameter value in the quadratic family z 7→ z + c. The principal nest of the Yoccoz parapuzzle pieces has rescaled asymptotic geometry equal to the filled-in Julia set of z 7→ z − 1. The modulus of two such successive parapuzzle pieces increases at a linear rate. Finally, we prove a “hairiness” theorem for the Mandelbrot set at the ...

this paper studies the use of unscented kalman filters (ukf) to estimate nonlinear dynamics and, specifically, adaptive determination of scaling parameters in these filters. due to lack of analytic solution and use of numerical methods instead, the computational load of these filters increases drastically. in this paper, a new method is proposed based on interactive multiple models (imm) which ...

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We derive an exact analytical criterion for the validity of single-parameter scaling in this model. According to this criterion, states with energies within the conduction band of the underlying nonrandom system satisfy sin...