We consider the energy spectrum of a quasigeostrophic model of forced, rotating turbulent flow. We provide a rigorous a priori bound E(k)<or=Ck(-2) valid for wave numbers that are smaller than a wave number associated with the forcing injection scale. This upper bound separates this spectrum from the Kolmogorov-Kraichnan k(-5/3) energy spectrum that is expected in a two-dimensional Navier-Stoke...

The spectrum of a Hamiltonian cycle (of a Gray code) in an n-dimensional Boolean cube is the series a = (a1, . . . , an), where ai is the number of edges of the ith direction in the cycle. The necessary conditions for the existence of a Gray code with the spectrum a are available: the numbers ai are even and, for k = 1, . . . , n, the sum of k arbitrary components of a is at least 2. We prove t...

This paper aims at providing a numerical calculation method of the spectrum of Lyapunov exponents in a four-dimensional impulsive hybrid nonlinear dynamics of a passive compass-gait model under the OGY control approach by means of a controlled hybrid Poincaré map. We present a four-dimensional simplified analytical expression of such hybrid map obtained by linearizing the uncontrolled impulsive...