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Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory
It is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter
Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces
There is a long standing conjecture in Hamiltonian analysis which claims that there exist at least $n$ geometrically distinct closed characteristics on every compact convex hypersurface in $\R^{2n}$
Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit
In this paper, using the Maslov index theory in symplectic geometry, we build up some stability criteria for symmetric periodic orbits in a Hamiltonian system, which is motivated by the recent
Stability analysis for standing pulse solutions to FitzHugh–Nagumo equations
This paper studies standing pulse solutions to the FitzHugh–Nagumo equations. Since the reaction terms are coupled in a skew-gradient structure, a standing pulse solution is a homoclinic orbit of a
Index theory for heteroclinic orbits of Hamiltonian systems
Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic
Stability Criteria for Reaction-Diffusion Systems with Skew-Gradient Structure
This paper deals with reaction-diffusion systems with skew-gradient structure. In connection with calculus of variations, we show that there is a close relation between the stability of a steady