In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, $$S'$$ S ′ , estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, $$S'$$ S ′ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.
Celestial Mechanics and Dynamical Astronomy – Springer Journals
Published: Apr 28, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
All the latest content is available, no embargo periods.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud