We present a method of proving existence of center manifolds within specified domains. The method is based on a combination of topological tools, normal forms, and rigorous computer-assisted computations. We apply our method to obtain a proof of a center manifold in an explicit region around the equilibrium point L1 in the Earth–Sun planar restricted circular three-body problem.

Keywords: Neutral delayed differential equation Double Hopf bifurcation Normal form Multiple time scales Center manifold reduction a b s t r a c t In this paper, we study dynamics in a container crane model with delayed position feedback , with particular attention focused on non-resonant double Hopf bifurcation. By using multiple time scales and center manifold reduction methods, we obtain the...

This paper concerns the minimax center of a collection linear subspaces. For k-dimensional subspaces an n-dimensional vector space, this can be cast as finding minimum enclosing ball on Grassmann manifold. differing dimension, setting becomes disjoint union Grassmannians rather than single manifold, and problem is no longer well-defined. However, natural geometric maps exist between these manif...

in this paper‎, ‎the‎ ‎authors prove that a strictly kähler-berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ kähler manifold‎.

The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar dif...

We study a codimension two steady-state/steady-state mode interaction with D4 symmetry, where the center manifold is three-dimensional. Primary branches of equilibria undergo secondary Hopf bifurcations to periodic solutions which undergo further bifurcations leading to chaotic dynamics. This is not an exponentially small effect, and the chaos obtained in simulations using DsTool is large-scale...