Hadamard-Perron theorems and effective hyperbolicity

Vaughn Climenhaga, Yakov Pesin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We prove several new versions of the Hadamard-Perron theorem, which relates infinitesimal dynamics to local dynamics for a sequence of local diffeomorphisms, and in particular establishes the existence of local stable and unstable manifolds. Our results imply the classical Hadamard-Perron theorem in both its uniform and non-uniform versions, but also apply much more generally. We introduce a notion of 'effective hyperbolicity' and show that if the rate of effective hyperbolicity is asymptotically positive, then the local manifolds are well behaved with positive asymptotic frequency. By applying effective hyperbolicity to finite-orbit segments, we prove a closing lemma whose conditions can be verified with a finite amount of information.

Original languageEnglish (US)
Pages (from-to)23-63
Number of pages41
JournalErgodic Theory and Dynamical Systems
StatePublished - Nov 17 2014

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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