Non-differentiability of Alpha function at the boundary of flat

TL;DR

This paper constructs a mechanical Hamiltonian system with a non-differentiable Alpha function at the boundary of a flat, demonstrating stability of this phenomenon under perturbations in systems with two degrees of freedom.

Contribution

It introduces a specific Hamiltonian system with a flat Alpha function boundary and proves the stability of non-differentiability under perturbations for two degrees of freedom.

Findings

Alpha function has a flat region with non-differentiability at its boundary.

The non-differentiability phenomenon is stable under perturbations in two-degree-of-freedom systems.

Constructs a Hamiltonian system demonstrating these properties.

Abstract

With the variational method introduced by J Mather, we construct a mechanical Hamiltonian system whose Alpha function has a flat F and is non-differentiable at the boundary of F. In the case of two degrees of freedom, we prove this phenomenon is stable under perturbations of Mane's