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A numerical study o...
A numerical study of infinitely renormalizable area-preserving maps
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- Gaidashev, Denis, 1973- (författare)
- Uppsala universitet,Analys och tillämpad matematik,CAPA
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- Johnson, Tomas, 1979- (författare)
- CAPA
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(creator_code:org_t)
- Informa UK Limited, 2012
- 2012
- Engelska.
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Ingår i: Dynamical systems. - : Informa UK Limited. - 1468-9367 .- 1468-9375. ; 27:3, s. 283-301
- Relaterad länk:
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http://arxiv.org/pdf...
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visa fler...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- It has been shown in Gaidashev and Johnson [D. Gaidashev and T. Johnson, Dynamics of the universal area-preserving map associated with period doubling: stable sets, J. Mod. Dyn. 3(4) (2009), pp. 555–587.] and Gaidashev et al. [D. Gaidashev, T. Johnson, and M. Martens, Rigidity for infinitely renormalizable area-preserving maps, in preparation.] that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Hölder continuous of exponent α > 0. In this article we investigate numerically the specific value of α. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- 37E20
- 37C15
- 37A20
- 37M99
- renormalization
- area-preserving maps
- rigidity
- co-cycles
- MATHEMATICS
- MATEMATIK
- Mathematics
- Matematik
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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