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.