The global superstability of a dynamical system is allowed when all bounded orbits of this system are superstable, .i.e. There exist a minus infinity Lyapunouv exponent. In this paper it is shown that any globally superstable 2-D quadratic map is conjugate to the 1D quadratic map. This result allow us to determine some forms of superstable 1-D quadratic maps.

LetX be a set with a binary operation ◦ such that, for each x, y, z ∈ X, either x ◦y ◦z x ◦z ◦y, or z◦ x◦y x◦ z◦y . We show the superstability of the functional equation g x◦y g x g y . More explicitly, if ε ≥ 0 and f : X → C satisfies |f x ◦ y − f x f y | ≤ ε for each x, y ∈ X, then f x ◦ y f x f y for all x, y ∈ X, or |f x | ≤ 1 √1 4ε /2 for all x ∈ X. In the latter case, the constant 1 √ 1 4...

In this paper, we establish the stability and superstability of J∗−derivations in J∗−algebras for the generalized Jensen–type functional equation rf( x+ y r ) + rf( x− y r ) = 2f(x). Finally, we investigate the stability of J∗−derivations by using the fixed point alternative.

In this paper, we will consider Hyers–Ulam–Rassias stability of multipliers and ring derivations between Banach algebras. As a corollary, we will prove superstability of ring derivations and multipliers. That is, approximate multipliers and approximate ring derivations are exact multipliers and ring derivations.

We reconsider the problem of absence of continuous symmetry breaking for systems of point particles in R. Assuming smoothness and suitable decay of the interaction, we show that each tempered Gibbs measure is invariant under translations. If the particles exhibit internal degrees of freedom with continuous symmetries, the latter are also preserved. The proof is elementary and avoids the use of ...

Abstract: The focal point of this paper is the design of fixed-order controllers for persistent disturbance rejection. It is shown that optimal controller design can, in this case, be formulated as a generalized eigenvalue problems. The results in this paper rely on an extension of the concepts of equalized performance and superstability to the case of multiinput/multi-output systems described ...