-adic chaos and random number generation.
-adic dynamical systems and formal groups
Packing dimensions, transversal mappings and geodesic flows.
Packing spectra for Bernoulli measures supported on Bedford-McMullen carpets
We consider the packing spectra for the local dimension of Bernoulli measures supported on Bedford-McMullen carpets. We show that typically the packing dimension of the regular set is smaller than the packing dimension of the attractor. We also consider a specific class of measures for which we are able to calculate the packing spectrum exactly, and we show that the packing spectrum is discontinuous as a function on the space of Bernoulli measures.
Painlevé analysis and similarity reductions for the magma equation.
Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation
Parabolic Cantor sets
The notion of a parabolic Cantor set is introduced allowing in the definition of hyperbolic Cantor sets some fixed points to have derivatives of modulus one. Such difference in the assumptions is reflected in geometric properties of these Cantor sets. It turns out that if the Hausdorff dimension of this set is denoted by h, then its h-dimensional Hausdorff measure vanishes but the h-dimensional packing measure is positive and finite. This latter measure can also be dynamically characterized as the...
Parabolic curves for diffeomorphisms in C2.
Parabolic curves in .
Parabolic orbifolds and the dimension of the maximal measure for rational maps.
Parallelepipeds, nilpotent groups and Gowers norms
In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions and and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.
Parameterized curve as attractors of some countable iterated function systems
In this paper we will demonstrate that, in some conditions, the attractor of a countable iterated function system is a parameterized curve. This fact results by generalizing a construction of J. E. Hutchinson [Hut81].
Parameters identification and synchronization of chaotic delayed systems containing uncertainties and time-varying delay.
Parametric mean curvature evolution with a Dirichlet boundary condition.
Parametrically excited nonlinear systems: A comparison of two methods.
Parapuzzle of the multibrot set and typical dynamics of unimodal maps
We study the parameter space of unicritical polynomials . For complex parameters, we prove that for Lebesgue almost every , the map is either hyperbolic or infinitely renormalizable. For real parameters, we prove that for Lebesgue almost every , the map is either hyperbolic, or Collet–Eckmann, or infinitely renormalizable. These results are based on controlling the spacing between consecutive elements in the “principal nest” of parapuzzle pieces.
Parry expansions of polynomial sequences.
Partial hyperbolicity and homoclinic tangencies
We show that any diffeomorphism of a compact manifold can be approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.
Partial hyperbolicity for symplectic diffeomorphisms
Partial hyperbolicity of G-induced flows.