The periodic orbit conjecture states that, on closed manifolds, the set of lengths orbits a non-vanishing vector field all whose are admits an upper bound. This is known to be false in general due counterexample by Sullivan. However, it satisfied under geometric condition being geodesible. In this work, we use recent characterization Eulerisable flows (or more generally admitting strongly adapt...

We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard’s corner point. We prove that smooth Hamiltonian flows which limit to this billiard have a nearby periodic orbit if and only if the polygon angles at the corner are ‘‘acceptable.’’ The criterion for...

We investigate the triangulated hull of orbit categories perfect derived category and bounded a ring concerning power suspension functor. It turns out that will correspond to full subcategory compact objects certain periodic complexes. This specializes Stai Zhao's result when is finite dimensional algebra with global dimension over field. As first application, if $A,B$ are flat algebras commuta...

Time-delay autosynchronization (TDAS) can be used to stabilize unstable periodic orbits in dynamical systems. The technique involves continuous feedback of signals delayed by the orbit's period. One variant, ETDAS, uses information further in the past. In both cases, the feedback signal vanishes on the target periodic orbit and hence the stabilized periodic orbit is one of the original dynamica...

Oneand two-parameter Hopf bifurcation behavior is analyzed for several variants of the Citri-Epstein mechanism of the chlorite-iodide reaction. The coefficients of an equation for the amplitude of oscillations (the universal unfolding of the Hopf bifurcation) are evaluated numerically. Local bifurcation diagrams and bifurcation sets are derived from the amplitude equation. Suband supercritical ...