Abstract
The theory of chaos and shadowing developed recently by the author is amplified to the case of a heteroclinically tubular cycle. Specifically, let F be a C 3 diffeomorphism on a Banach space. F has a heteroclinically tubular cycle that connects two normally hyperbolic invariant manifolds. Around the heteroclinically tubular cycle, a Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. As an example, a sine-Gordon equation with a chaotic forcing is studied. Existence of a heteroclinically tubular cycle is proved. Also proved are chaos associated with the heteroclinically tubular cycle, and chaos cascade referring to the embeddings of smaller-scale chaos in larger-scale chaos.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
