Hamiltonian systems with orbits covering densely submanifolds of small codimension

✍ Scribed by Ernest Fontich; Pau Martı́n

• Book ID: 104330371
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 152 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00115-3

✦ Synopsis

The existence of a transition chain in a Hamiltonian system leads to the existence of orbits shadowing it, if some lambda lemma can be applied. This fact has been used to prove the existence of di usion in perturbations of integrable a priori stable systems. We prove that, under suitable conditions, there are orbits which cover densely codimension two submanifolds of the (2n -1)-dimensional energy level. We also construct examples, near general integrable systems, where the computations to verify the su cient conditions for the appearance of such phenomenon can be performed.