European Workshop "Nonlinear Maps and Applications" - 2017, Nizhni Novgorod, Russia

Regular European Workshops "Nonlinear Maps and Applications" (NOMA) are held biannually in those European Universities where successful researchers in the area of nonlinear maps and their applications work. In far 1973 year French scientist Christian Mira organized Colloquium "Point Mappings and Applications" in the University of Toulouse, where he worked. According to Christian Mira, his mathematical preferences were formed under the influence of works of the founder of the Nizhni Novgorod nonlinear oscillations school A.A. Andronov

Dynamic Separation of Chaotic Signals in the Presence of Noise

The problem of separation of an observed sum of chaotic signals into the individual components in the presence of noise on the path to the observer is considered. A noise threshold is found above which high-quality separation is impossible. Below the threshold, each signal is recovered with any prescribed accuracy. This effect is shown to be associated with the information content of the chaotic signals and a theoretical estimate is given for the threshold.Comment: PDF, 12 pages, 6 figures, submitted to Phys. Rev.

Example of the Smooth Skew Product in the Plane with the One-dimensional Ramified Continuum as the Global Attractor

The example is constructed of the C1-smooth skew product of interval maps possessing the one-dimensional ramified continuum (containing no arcs homeomorphic to the circle) with an infinite set of ramification points as the global attractor

Invariant Curves of Quadratic Maps of the Plane from the One-Parameter Family Containing the Trace Map

The rigorous proofs are given: (1) for the existence of the unbounded invariant curves, containing the fixed point – source (μ + 1; 1), of the maps from the one-parameter family Fμ(x,y) = (xy, (x − μ)2), μ ∈ [0, 2]; (2) for the birth of the closed invariant curve from the elliptic fixed point (μ − 1; 1) for μ = 3 / 2. Numerical results are presented for the main steps of the evolution of this invariant curve, when μ changes in the interval (3 / 2, 2)

Invariant Curves of Quadratic Maps of the Plane from the One-Parameter Family Containing the Trace Map*

The rigorous proofs are given: (1) for the existence of the unbounded invariant curves, containing the fixed point – source (μ + 1; 1), of the maps from the one-parameter family Fμ(x,y) = (xy, (x − μ)2), μ ∈ [0, 2]; (2) for the birth of the closed invariant curve from the elliptic fixed point (μ − 1; 1) for μ = 3 / 2. Numerical results are presented for the main steps of the evolution of this invariant curve, when μ changes in the interval (3 / 2, 2)