  We present a general theory of exceptional points of degeneracy (EPD) in
periodically time-variant systems that do not necessarily require the presence
of loss or gain, and we show that even a single resonator with a time-periodic
component may develop EPDs. An EPD is a special point in a system parameter
space at which two or more eigenmodes coalesce in both their eigenvalues and
eigenvectors into a single degenerate eigenmode. We demonstrate the conditions
for EPDs to exist in time-periodic systems that are either lossless/gainless or
with loss and/or gain and we show that a system with zero time-average
loss/gain exhibits EPDs with purely real resonance frequencies, yet the
resonator energy grows algebraically in time. We show the occurrence of EPDs in
a single LC resonator while the introduced concept is general for any
time-periodic system. These findings have significant importance in various
electromagnetic/photonic systems and pave the way of applications in areas of
sensors, amplifiers and modulators. A potential application of this time
varying EPD is highlighted as a highly-sensitive sensor.
