Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Stefano Luzzatto"'
We develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of one-dimensional maps $f_a (x) = a - x^2$. We illustrate the effectivenes
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ec17d69007f5555dfd6a8e1a83b8d1f
http://arxiv.org/abs/2004.13444
http://arxiv.org/abs/2004.13444
We give geometric conditions that are necessary and sufficient for the existence of Sinai-Ruelle-Bowen (SRB) measures for $C^{1+\alpha}$ surface diffeomorphisms, thus proving a version of the Viana conjecture. As part of our argument we give an origi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7916786753ca86677cf4a5b785b7d733
Publikováno v:
Experimental Mathematics. 25:116-124
We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter values in the quadratic family. We first compute a radius of the critic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5a8d042ade45d37c080f3b8f71953e27
https://doi.org/10.1080/10586458.2015.1048011
https://doi.org/10.1080/10586458.2015.1048011
Publikováno v:
Dynamical Systems. 31:79-88
We derive some new conditions for integrability of dynamically defined C^1 invariant splittings in arbitrary dimension and co-dimension. In particular we prove that every 2-dimensional C^1 invariant decomposition on a 3-dimensional manifold satisfyin
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e292ce661cae4635e514d9c5b185a469
https://doi.org/10.1080/14689367.2015.1057480
https://doi.org/10.1080/14689367.2015.1057480
Publikováno v:
Proceedings of the American Mathematical Society. 141:3157-3169
We show that for any C 1 + α C^{1+\alpha } diffeomorphism of a compact Riemannian manifold, every non-atomic, ergodic, invariant probability measure with non-zero Lyapunov exponents is approximated by uniformly hyperbolic sets in the sense that ther
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https://explore.openaire.eu/search/publication?articleId=doi_________::8acd37ea827107b5c0ec9ff8a1511ee5
https://doi.org/10.1090/s0002-9939-2013-11565-0
https://doi.org/10.1090/s0002-9939-2013-11565-0
We give new sufficient conditions for the integrability and unique integrability of continuous tangent sub-bundles on manifolds of arbitrary dimension, generalizing Frobenius' classical Theorem for C^1 sub-bundles. Using these conditions we derive ne
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ba6b523d08e6fde7bf5b465971abef8e
http://hdl.handle.net/10044/1/38929
http://hdl.handle.net/10044/1/38929
An important class of `physically relevant' measures for dynamical systems with hyperbolic behavior is given by Sinai-Ruelle-Bowen (SRB) measures. We survey various techniques for constructing SRB measures and studying their properties, paying specia
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f5d0feb1e7a7d29125c6db4694a6aef
Autor:
Stefano Luzzatto, Katie Bloor
Publikováno v:
International Journal of Bifurcation and Chaos. 19:2213-2232
We define and compute hyperbolic coordinates and associated foliations which provide a new way to describe the geometry of the standard map. We also identify a uniformly hyperbolic region and a complementary 'critical' region containing a smooth curv
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5aff5796bba550c6bcf708c442efa6cb
https://doi.org/10.1142/s0218127409024025
https://doi.org/10.1142/s0218127409024025
Publikováno v:
Ergodic Theory and Dynamical Systems. 28:1049-1080
We consider C^{2} Henon-like families of diffeomorphisms of R^{2} and study the boundary of the region of parameter values for which the nonwandering set is uniformly hyperbolic. Assuming sufficient dissipativity, we show that the loss of hyperbolici
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f04977d946a3bc47332c4fe280de8740
https://doi.org/10.1017/s0143385707000776
https://doi.org/10.1017/s0143385707000776
Autor:
Sarah Day, Hiroe Oka, Hiroshi Kokubu, Konstantin Mischaikow, Paweł Pilarczyk, Stefano Luzzatto
Publikováno v:
Nonlinearity. 21:1967-1987
We develop a rigorous computational method for estimating the Lyapunov exponents in uniformly expanding regions of the phase space for one-dimensional maps. Our method uses rigorous numerics and graph algorithms to provide results that are mathematic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::99b1d3c35567c81a90a36ee079432e56
https://doi.org/10.1088/0951-7715/21/9/002
https://doi.org/10.1088/0951-7715/21/9/002