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Which planetary boundary when stabilized would cause increased stability in other boundaries?

Hyperbolic group

Boundary value problem

Gromov boundary

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Stabilizing the Lagrange stability boundary in planetary systems would lead to increased stability in other boundaries. Research indicates that while Hill stability requires planet ordering to remain constant, Lagrange stability demands all planets to stay bound to the central star . In non-resonant systems, the Hill and Lagrange stability boundaries are closely aligned, but in resonant systems, they diverge significantly . Interestingly, the region of stability in resonant interactions is unexpectedly larger than predicted by the Hill stability formula, encompassing most known resonant interactions . This finding has implications for understanding planetary system dynamics and offers new insights into planet formation models by highlighting the importance of quantifying dynamical interactions near stability boundaries .

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Open access•Proceedings Article•DOI Boundary stabilization of an anti-stable wave equation with in-domain anti-damping Andrey Smyshlyaev, Eduardo Cerpa, Miroslav Krstic - Show less +2 more 01 Dec 2009	Stabilizing the anti-damping boundary in the wave equation enhances overall stability by shifting eigenvalues to the right half-plane, impacting the system's dynamics positively.
Open access•Journal Article•DOI Stability Limits in Resonant Planetary Systems Rory Barnes, Richard Greenberg - Show less +1 more 27 Jul 2007-The Astrophysical Journal 68 Citations	Stabilizing the Lagrange boundary in resonant planetary systems increases overall stability, impacting the proximity to the Hill stability boundary and enhancing system stability.
Open access•Posted Content Stability for hyperbolic groups acting on boundary spheres Kathryn Mann, Jason Fox Manning - Show less +1 more 02 Apr 2021-arXiv: Geometric Topology	Not addressed in the paper.
Open access•Posted Content Stabilisation by noise on the boundary for a Chafee-Infante equation with dynamical boundary conditions Klemens Fellner, Stefanie Sonner, Bao Quoc Tang, Do Duc Thuan - Show less +3 more 29 Mar 2018-arXiv: Analysis of PDEs	Not addressed in the paper.
Journal Article•DOI Studying the stability boundaries of the gyro-stabilized satellite on a circular orbit M. A. Novikov 01 Apr 2009-Automation and Remote Control	Stabilizing the second part of the stability boundary, where conditions become equalities, increases stability in other boundaries of the gyro-stabilized satellite on a circular orbit.

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