abstr8
In practical experiments, e.g.,
with neuron cells, one typically observes only a few components
of a higher-dimensional system, or even only one component. For example,
one measures the output voltage of a neuron, the state of which is determined
by many further variables.
Assume that the high-dimensional system has a periodic trajectory and an
associated Poincaré map P. We explain the connection
between the map P and the orbits of another map, which arises
from the interpretation of one-dimensional data as return times.
We prove that these maps are locally conjugate by a transformation
which generically is a diffeomorphism.