Synthesizing chaotic maps with prescribed invariant densities

Synthesizing Chaotic Maps with Prescribed Invariant Densities

The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.

Sets with Prescribed Arithmetic Densities

Using concepts of generalized asymptotic and logarithmic densities based on weighted arithmetic means over an arithmetical semigroup G we prove that under some additional technical assumptions on the weighted counting function of its elements, a subset of G exists with all four generalized densities (upper and lower asymptotic and logarithmic) prescribed subject to the natural condition 0 ≤ d(A...

Hierarchy of random deterministic chaotic maps with an invariant measure

Hierarchy of one and many-parameter families of random trigonometric chaotic maps and one-parameter random elliptic chaotic maps of cn type with an invariant measure have been introduced. Using the invariant measure (Sinai-Ruelle-Bowen measure), the Kolmogrov-Sinai entropy of the random chaotic maps have been calculated analytically, where the numerical simulations support the results .

Scaling properties of invariant densities of coupled Chebyshev maps

We study 1-dimensional coupled map lattices consisting of diffusively coupled Chebyshev maps of N -th order. For small coupling constants a we determine the invariant 1-point and 2-point densities of these nonhyperbolic systems in a perturbative way. For arbitrarily small couplings a > 0 the densities exhibit a selfsimilar cascade of patterns, which we analyse in detail. We prove that there are...

Orthonormal Expansions of Invariant Densities for Expanding Maps