m-SMOOTHNESS OF INVARIANT FIBER BUNDLES FOR DYNAMIC EQUATIONS ON MEASURE CHAINS
نویسنده
چکیده
We present a new self-contained and rigorous proof of the smoothness of invariant fiber bundles for dynamic equations on measure chains or time scales. Here, an invariant fiber bundle is the generalization of an invariant manifold to the nonautonomous case. Our main result generalizes the “Hadamard-Perron theorem” to the time-dependent, infinitedimensional, noninvertible, and parameter-dependent case, where the linear part is not necessarily hyperbolic with variable growth rates. As a key feature, our proof works without using complicated technical tools.
منابع مشابه
Reduction in Principal Fiber Bundles: Covariant Euler-poincaré Equations
Let π : P → Mn be a principal G-bundle, and let L : JP → Λn(M) be a G-invariant Lagrangian density. We obtain the Euler-Poincaré equations for the reduced Lagrangian l defined on C(P ), the bundle of connections on P .
متن کاملThe Effect of Fiber Breakage on Transient Stress Distribution in a Single-Lap Joint Composite Material
In the present study, the transient stress distribution caused by a break in the fibers of an adhesive bonding is investigated. Transient stress is a dynamic response of the system to any discontinuity in the fibers from detachment time till their equilibrium state (or steady state). To derive the governing dynamic equilibrium equations shear lag model is used. Here, it is assumed that the tens...
متن کاملInvariant Foliations and Stability in Critical Cases
We construct invariant foliations of the extended state space for nonautonomous semilinear dynamic equations on measure chains (time scales). These equations allow a specific parameter dependence which is the key to obtain perturbation results necessary for applications to an analytical discretization theory of ODEs. Using these invariant foliations we deduce a version of the Pliss reduction pr...
متن کاملFiber bundles and Lie algebras of top spaces
In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.
متن کاملDynamic stress concentration in a hybrid composite laminate subjected to a sudden internal break
In this work, transient dynamic stress concentration in a hybrid composite laminate subjected to a sudden internal crack is examined. It is assumed that all fibers lie in one direction and the applied load acts along direction of fibers. Two types arrangements are considered for the fiber; square and hexagonal arrangement. Using shear lag model, equilibrium equations are deduced and upon proper...
متن کامل