Linear instability of periodic orbits of free period Lagrangian systems

Relative Periodic Orbits of Symmetric Lagrangian Systems

Large minimal period orbits of periodic autonomous systems *

We prove the existence of periodic orbits with minimal period greater than any prescribed number for a natural Lagrangian autonomous system in several variables that is analytic and periodic in each variable and whose potential is nonconstant. Mathematics Subject Classification: 34C25, 37J45

Optimal periodic orbits of chaotic systems occur at low period.

Invariant sets embedded in a chaotic attractor can generate time averages that diier from the average generated by typical orbits on the attractor. Motivated by two diierent topics (namely, controlling chaos and riddled basins of attraction), we consider the question of which invariant set yields the largest (optimal) value of an average of a given smooth function of the system state. We presen...

Periodic orbits from Δ-modulation of stable linear systems

The -modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by where 0 is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of a finite order. Some concrete results about the existence of a certain order of periodic points are also derived. We also study th...

Periodic Orbits of Hamiltonian Systems

5 The Variational principles and periodic orbits 21 5.1 Lagrangian view point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2 Hamiltonian view point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.3 Fixed energy problem, the Hill’s region . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.4 Continuation of periodic orbits as critical p...