Sentence examples for exists invariant from inspiring English sources

The natural question is when the condition is not satisfied, that is, there is some such that whether there exists invariant curve for mapping (3.5), whether its frequency can persist without any drift.

If the Ergodicity Assumption holds, then, for any arbitrary policy a, there exists an invariant measure p a, i.e. the unique invariant probability measure satisfying begin{array}rcl@ p_{mathbf{a}}(B =int_{mathbf{S}}mathbf{T}_{f}(B|s p_{f}(dx), end{array} (60).

Then there exists an invariant measure η of (X t)).

(3) There exists an invariant dimension-measure on ({mathcal A}) associated to some linear basis.  .

In the case of persistence, we prove that there exists an invariant distribution which is ergodic.

Under the given conditions, there exists an invariant manifold associated to (f_0) inside the fixed fiber.

In the case of persistence, they proved that there exists an invariant distribution which is ergodic.

There exists an invariant subspace Z of E with dimension i(A0) and some r > 0 such that J y) < 0 whenever y ∈ Z and ||y||1 = r.

In particular, we show that there exists an invariant rectangle that attracts all the solutions of system (1.2) regardless of the initial values.

If not, for any sufficiently small ϵ, there exists some invariant set W ((Wsubset U)) such that (Wsetminus E_{0}) is not empty.

It is shown that there exists an invariant torus via Hopf bifurcation and period 4 4 motions via subharmonic bifurcation as two controlling parameters varying near the critical point for the resonance λ04= 1, and that there exists an invariant circle and unstable fixed points of order 3 bifurcating from the fixed point, and the system leads eventually to chaos in the resonance λ03="1.