We consider a special class of Lagrangians that play a fundamental role in the theory of second order Lagrangian systems: Twist systems. This subclass of Lagrangian systems is deened via a convenientâ€¦ (More)

On the energy manifolds of fourth order conservative systems closed characteristics can be found in many cases via analogues of Twist-maps. The 'Twist property' implies the existence of a generatingâ€¦ (More)

We study the existence of closed characteristics on threedim nsional energy manifolds of second-order Lagrangian systems. These m anifolds are always noncompact, connected, and not necessarily ofâ€¦ (More)

We show that some very naturally occurring energy manifolds that are induced by second-order Lagrangians L = L(u, uâ€², uâ€²â€²) are not, in general, of contact type in (R4, Ï‰). We also comment on the moreâ€¦ (More)

The comparison principle for scalar second order parabolic PDEs on functions u(t, x) admits a topological interpretation: pairs of solutions, u1(t, Â·) and u2(t, Â·), evolve so as to not increase theâ€¦ (More)

We consider fourth order parabolic equations of gradient type. For sake of simplicity the analysis is carried out for the specific equation ut = âˆ’Î³uxxxx + Î²uxx âˆ’ F (u), with (t, x) âˆˆ (0,âˆž) Ã— (0, L)â€¦ (More)

We study forcing of periodic points in orientation reversing twist maps. First, we observe that the fourth iterate of an orientation reversing twist map can be expressed as the composition of fourâ€¦ (More)

For a large class of second order Lagrangian dynamics, one may reformulate the problem of finding periodic solutions as a problem in solving second-order recurrence relations satisfying a twistâ€¦ (More)

In second order Lagrangian systems bifurcation branches of periodic solutions preserve certain topological invariants. These invariants are based on the observation t hat periodic orbits of a secondâ€¦ (More)

The comparison principle for scalar second order parabolic PDEs on functions u(t, x) admits a topological interpretation: pairs of solutions, u(t, Â·) and u(t, Â·), evolve so as to not increase theâ€¦ (More)