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035			_aocm51338542
040			_aP5A _cP5A
090			_acs
100	1		_aGuardia, Marcel _u(Institut Mathématiques de Jussieu, France) _96050
245	1	4	_aThe quasi-ergodic hypothesis and Arnol'd diffusion in nearly integrable Hamiltonian systems/ _cMarcel Guardia.
246	1		_aMinicurso: The quasi-ergodic hypothesis and Arnol'd diffusion in nearly integrable Hamiltonian systems
260			_aRio de Janeiro: _bIMPA, _c2013.
300			_avideo online
500			_aMini Course - 5 classes
505	2		_aThe quasi-ergodic hypothesis, proposed by Ehrenfest and Birkhoff, says that a typical Hamiltonian system on a typical energy surface has a dense orbit. This question is wide open. In the early sixties, V. Arnold constructed a nearly integrable Hamiltonian system presenting instabilities and he conjectured that such instabilities existed in typical nearly integrable Hamiltonian systems. A proof of Arnold's conjecture in two and half degrees of freedom was announced by J. Mather in 2003. In these lectures I will explain a recent proof of Arnol'd conjecture for two and a half degrees of freedom systems based on two works, which use a different approach. One by V. Kaloshin, P. Bernard and K. Zhang, and another by V. Kaloshin and K. Zhang. Their approach is based on constructing a net of normally hyperbolic invariant cylinders and a version of Mather variational method. In these lectures I will also explain a more recent work by myself and V. Kaloshin. In this work, using also this approach, we prove a weak form of the quasi-ergodic hypothesis. We prove that for a dense set of non-autonomous perturbations of two degrees of freedom Hamiltonian systems there exist unstable orbits which accumulate in a set of positive measure containing KAM tori.
650	0	4	_aMatematica. _2larpcal _919899
697			_aCongressos e Seminários. _923755
856	4		_zCLASS 1 _uhttps://www.youtube.com/watch?v=8dk0vcjC1nw&index=1&list=PLo4jXE-LdDTTbk5dqhvMPb3liizziPJtO
856	4		_zCLASS 2 _uhttps://www.youtube.com/watch?v=OUZW0R-ko64&index=2&list=PLo4jXE-LdDTTbk5dqhvMPb3liizziPJtO
856	4		_zCLASS 3 _uhttps://www.youtube.com/watch?v=u7OUBEfjZU0&index=3&list=PLo4jXE-LdDTTbk5dqhvMPb3liizziPJtO
856	4		_zCLASS 4 _uhttps://www.youtube.com/watch?v=3VGC1Ayxv9g&index=4&list=PLo4jXE-LdDTTbk5dqhvMPb3liizziPJtO
856	4		_zCLASS 5 _uhttps://www.youtube.com/watch?v=7dNMjieTLrc&index=5&list=PLo4jXE-LdDTTbk5dqhvMPb3liizziPJtO
942			_2ddc _cBK
999			_aTHE QUASI-ERGODIC hypothesis and Arnol'd diffusion in nearly integrable Hamiltonian systems. Marcel Guardia. Rio de Janeiro: IMPA, 2013. video online. Disponível em: <https://www.youtube.com/watch?v=8dk0vcjC1nw&index=1&list=PLo4jXE-LdDTTbk5dqhvMPb3liizziPJtO>. Acesso em: 27 nov. 2014. _c34197 _d34197