5 problems

The compactified system is obtained from a nonautonomous system with autonomous future and past limit systems, and the equilibria of those limit systems correspond to equilibria of…

Let $A^+$ and $A^-$ be general normally hyperbolic compact invariant sets of the respective limit systems. Invariant manifold extension conjecture. The statements for equilibria in…

Let $P_n(x,y)$ and $Q_n(x,y)$ be polynomials of degree $n$, defining the planar polynomial system … An invariant line is a straight line preserved by the flow of this system. Ye's…

In the Sitnikov problem, let $e\in(0,1)$ denote the eccentricity, and in the restricted planar three-body problem (RPTBP), let $\mu\in(0,1/2]$ denote the mass parameter. An invaria…

Let $f\colon M\to M$ be a $C^1$-diffeomorphism, and let $Orb(p)$ be an orbit with well-defined non-vanishing Lyapunov exponents. In the two-dimensional case, assume that … Here…