Time Periodicity and Spatio-Temporal Symmetry
Part of the Progress in Mathematics book series (PM, volume 200)
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After steady states, the next simplest type of dynamics is periodic behavior, in which the state of the system repeats after some fixed interval of time. That is, the solution x(t) satisfies
where 0 < T ∈ R is the period. We also say that x is T-periodic. When discussing PDEs we often use the phrase ‘time-periodic’ to distinguish between such a state and one with spatially periodic patterning. This chapter focuses on periodic states in symmetric dynamical systems, a particularly rich area of equivariant dynamics.
$$ x(t + T) = x(t) for all t \in R $$
KeywordsPeriodic Solution Isotropy Subgroup Time Periodicity Unidirectional Ring Bidirectional Ring
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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