Journal Article10.1007/BF02762799
On sets of Haar measure zero in abelian polish groups
309
TL;DR: In this paper, the concept of zero set for the Haar measure can be generalized to abelian Polish groups which are not necessarily locally compact, and it turns out that these groups, in many respects, behave like locally compact groups.
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Abstract: It is shown that the concept of zero set for the Haar measure can be generalized to abelian Polish groups which are not necessarily locally compact. It turns out that these groups, in many respects, behave like locally compact groups. Suitably modified, many theorems from harmonic analysis carry over to this case. A few applications are given and some open problems are mentioned.
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Citations
Prevalence of exponential stability among nearly integrable Hamiltonian systems
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•Journal Article
On Haar null sets
TL;DR: In this article, it was shown that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of pairwise disjoint universally measurable sets which are not Haarnull.
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Generic Nekhoroshev theory without small divisors
TL;DR: In this article, a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems is presented. But this approach is restricted to generic integrable Hamiltonians and cannot handle generic nonanalytic Hamiltonians.
Ergodic optimization of Birkhoff averages and Lyapunov exponents
Jairo Bochi
- 01 May 2019
TL;DR: Ergodic optimization is the study of extremal values of asymptotic dynamical quantities such as Birkhoff averages or Lyapunov exponents, and of the orbits or invariant measures that attain them as discussed by the authors.
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•Posted Content
Generic Nekhoroshev theory without small divisors
TL;DR: In this article, a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems is presented. But this approach is restricted to generic integrable Hamiltonians and cannot handle generic nonanalytic Hamiltonians.
References
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