On two-parametric systems of matrices and diffeomorphisms
On univoque points for self-similar sets
Let K ⊆ ℝ be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method...
On zeta function and scattering poles for several convex bodies
On Ω-stability and structural stability of endomorphisms satisfying Axiom A
One sided branching in Anosov foliations.
One-dimensional chain recurrent sets of flows in the 2-sphere.
One-parameter families of brake orbits in dynamical systems
We give a clear and systematic exposition of one-parameter families of brake orbits in dynamical systems on product vector bundles (where the fiber has the same dimension as the base manifold). A generalized definition of a brake orbit is given, and the relationship between brake orbits and periodic orbits is discussed. The brake equation, which implicitly encodes information about the brake orbits of a dynamical system, is defined. Using the brake equation, a one-parameter family of brake orbits...
One-Parameter Flows with the Pseudo Orbit Tracing Property.
On-off intermittency in continuum systems driven by the Chen system
Previous studies on on-off intermittency in continuum systems are generally based on the synchronization of identical chaotic oscillators or in nonlinear systems driven by the Duffing oscillator. In this paper, one-state on-off intermittency and two-state on-off intermittency are observed in two five- dimensional continuum systems, respectively, where each system has a two- dimensional subsystem driven by the chaotic Chen system. The phenomenon of intermingled basins is observed below the blowout...
Optimality of Ruelle's bound for the domain of meromorphy of generalized zeta functions
Orbifold-Uniformizing Differential Equations.
Orbifold-Uniformizing Differential Equations. III. Arrangements Defined by 3-Dimensional Primitive Unitary Reflection Groups.
Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature.
Orbits connecting singular points in the plane
This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed.
Orientation Reversing Morse-Smale Diffeomorphisms of S2.
-adic dynamical systems and formal groups
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.
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...
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].
Parametric mean curvature evolution with a Dirichlet boundary condition.