S ep 2 01 6 Maslov-type indices and linear stability of elliptic Eulersolutions of the three-body problem
In this paper, we use the central configuration coordinate de composition to study the linearized Hamiltonian system near the 3-body elliptic Euler solution s. Then using the Maslov-type ω-index theory of symplectic paths and the theory of linear operators we compute theω-indices and obtain certain properties of linear stability of the Euler elliptic soluti ons of the classical three-body problem.
Bott formula of the Maslov-type index theory
In this paper the integer valued !-index theory parameterized by all ! on the unit circle for paths in the symplectic group Sp(2n) is established. Based on this index theory, the Bott formula of the Maslov-type index theory for iterated paths in Sp(2n) is estalished, the mean index for periodic solutions of Hamiltonian systems is dened, and the increasing estimate of the iterated Maslov-type index in terms of the mean index is proved.
Tethering the Administrative State: The Case Against Chevron Deference for FCC Jurisdictional Claims
Like many other agencies, the Federal Communications Commission has seen significant regulatory growth under President Obama. But unlike health care, financial reform, and other areas, this growth has come without statutory guidance from Congress. The FCC’s assertion of jurisdiction over broadband service is reminiscent of its earlier attempts to regulate cable and to deregulate telephone service, efforts that courts have viewed skeptically in the absence of specific statutory authorization. But this skepticism is in tension with Chevron, which grants agencies substantial deference to interpret ambiguities in the statutes that they administer. This article argues that Chevron deference should not extend to agency jurisdictional claims, such as the FCC’s claim to authority over broadband. For both constitutional and policy reasons, courts should distinguish between agency action that fills a gap in a statutory scheme and action that defines the outer boundary of that scheme. As the Commission’s net neutrality project winds its way through the judicial system, courts should not allow the agency to define the limits of its own authority, and should instead search closely for a grant of authority from Congress.