integrate

Examples of integrable

integrable
In a series of papers in the 1970s he illuminated a number of completely integrable systems, and established connections between them.
Note that one can apply this approach to a conjugacy between two partially hyperbolic diffeomorphisms having integrable center distributions (say, with compact leaves).
Among his famous successes is the geodesic flow on an ellipsoid, which he found to be integrable.
One can restrict of course to the unit bundle, that is consider normalized integrable quadratic differentials.
These identities contain information on the formal degree of square-integrable representations and on their position in the induced representation.
From (60) we can show that h(q) is square integrable.
Unfortunately, (41) is not integrable, but it can be evaluated for long times.
The time-one map of is non-jointly integrable if and only if it is accessible.
We emphasize that our approach works in arbitrarily many degrees of freedom and that it is independent of the integrable geometry one starts with.
Our construction, however, is independent of any integrable approximation.
However, no integrable solution of these equations has yet been found and one must resort to numerical methods.
One situation in which this approach works is the completely integrable case.
However, an involutive distribution is not integrable in general (see 2.1 for counter-examples).
These examples of systems which are integrable but not completely integrable are certainly very special and artificial.
In particular, they proved that there are invariant compact subsets in the space of integrable functions, which consist of functions of bounded variation.
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.