
We characterize the existence of first integrals and invariants (first integrals depending on the time) for the polynomial vector fields which are invariant under an involution.
First integrals, involutions, Invariants, Explicit solutions, first integrals of ordinary differential equations, first integrals, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, polynomial systems, Involutions, invariants, Symmetries, invariants of ordinary differential equations, Polynomial systems
First integrals, involutions, Invariants, Explicit solutions, first integrals of ordinary differential equations, first integrals, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, polynomial systems, Involutions, invariants, Symmetries, invariants of ordinary differential equations, Polynomial systems
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