Newton, Chebyshev, and Halley Basins of Attraction; A Complete Geometric Approach
Nombres self normaux
Nous inspirant de la construction de Champernowne d’un nombre normal en base 10 nous construisons un ensemble de nombres “self-normaux“ au sens de Schmeling ; cet ensemble est non dénombrable et dense dans .
Non equivalence of NMS flows on
We build the flows of non singular Morse-Smale systems on the 3-sphere from its round handle decomposition. We show the existence of flows corresponding to the same link of periodic orbits that are non equivalent. So, the link of periodic orbits is not in a 1-1 correspondence with this type of flows and we search for other topological invariants such as the associated dual graph.
Nonabsolutely Continuous Foliations for an Anosov Diffeomorphism.
Noncommutative algebras for hyperbolic diffeomorphisms.
Nonconventional limit theorems in averaging
We consider “nonconventional” averaging setup in the form , where , is either a stochastic process or a dynamical system with sufficiently fast mixing while , and , grow faster than linearly. We show that the properly normalized error term in the “nonconventional” averaging principle is asymptotically Gaussian.
Nonhyperbolic persistent attractors near the Morse–Smale boundary
Nonlinear control of chaotic systems: a switching manifold approach.
Nonlinear dynamics and chaos in a fractional-order HIV model.
Nonlinear filtering of oscillatory measurements in cardiovascular applications.
Nonsingular cocycles and piecewise linear time changes.
Nonuniform center bunching and the genericity of ergodicity among partially hyperbolic symplectomorphisms
We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns–Wilkinson and Avila–Santamaria–Viana. Combining this new technique with other constructions we prove that -generic partially hyperbolic symplectomorphisms are ergodic. We also construct new examples of stably ergodic partially hyperbolic diffeomorphisms.
Non-uniformly expanding dynamics in maps with singularities and criticalities
Non-uniformly hyperbolic billiards
Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles
In the present paper, we advance considerably the current knowledge on the topic of bifurcations of heteroclinic cycles for smooth, meaning C ∞, parametrized families {g t ∣t∈ℝ} of surface diffeomorphisms. We assume that a quadratic tangency q is formed at t=0 between the stable and unstable lines of two periodic points, not belonging to the same orbit, of a (uniformly hyperbolic) horseshoe K (see an example at the Introduction) and that such lines cross each other with positive relative speed as...
Nonwandering operators in Banach space.
Normal points for generic hyperbolic maps
We consider families of hyperbolic maps and describe conditions for a fixed reference point to have its orbit evenly distributed for maps corresponding to generic parameter values.
Obtuse triangular billiards. I: Near the triangle.
Off-center reflections: caustics and chaos.
On a one-dimensional analogue of the Smale horseshoe
We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then for Lebesgue-a.e. x.