| 21. |
- Faber, Carel, et al.
(författare)
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Relative maps and tautological classes
- 2005
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 7:1, s. 13-49
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Tidskriftsartikel (refereegranskat)
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| 22. |
- Farré Puiggalí, Gerard, et al.
(författare)
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Instabilities of invariant quasi-periodic tori
- 2022
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855 .- 1435-9863. ; 24:12, s. 4363-4383
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Tidskriftsartikel (refereegranskat)abstract
- We prove the existence of real analytic Hamiltonians with topologically unstable quasi -periodic invariant tori. Using various versions of our examples, we solve the following problems in the stability theory of analytic quasi-periodic motion:(1) Show the existence of topologically unstable tori of arbitrary frequency. Moreover, the Birkhoff Normal Form at the invariant torus can be chosen to be convergent, equal to a planar or non -planar polynomial.(2) Show the optimality of the exponential stability for Diophantine tori.(3) Show the existence of real analytic Hamiltonians that are integrable on half of the phase space, and such that all orbits on the other half accumulate at infinity.(4) For sufficiently Liouville vectors, obtain invariant tori that are not accumulated by a positive measure set of quasi-periodic invariant tori.
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| 23. |
- Gaidashev, Denis, 1973-, et al.
(författare)
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Renormalization and Siegel disks for complex Henon maps
- 2021
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 23:4, s. 1053-1073
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Tidskriftsartikel (refereegranskat)abstract
- We use hyperbolicity of golden-mean renormalization of dissipative Henon-like maps to prove that the boundaries of Siegel disks of sufficiently dissipative quadratic complex Henon maps with golden-mean rotation number are topological circles. Conditionally on an appropriate renormalization hyperbolicity property, we derive the same result for Siegel disks of Henon maps with all eventually periodic rotation numbers.
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| 24. |
- Gouezel, Sebastien, et al.
(författare)
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Subadditive and multiplicative ergodic theorems
- 2020
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Ingår i: Journal of the European Mathematical Society (Print). - : EUROPEAN MATHEMATICAL SOC. - 1435-9855 .- 1435-9863. ; 22:6, s. 1893-1915
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Tidskriftsartikel (refereegranskat)abstract
- A result for subadditive ergodic cocycles is proved that provides more delicate information than Kingman's subadditive ergodic theorem. As an application we deduce a multiplicative ergodic theorem generalizing an earlier result of Karlsson-Ledrappier, showing that the growth of a random product of semicontractions is always directed by some horofunction. We discuss applications of this result to ergodic cocycles of bounded linear operators, holomorphic maps and topical operators, as well as a random mean ergodic theorem.
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| 25. |
- Hedenmalm, Håkan, 1961-, et al.
(författare)
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The Klein-Gordon equation, the Hilbert transform, and dynamics of Gauss-type maps
- 2020
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855 .- 1435-9863. ; 22:6, s. 1703-1757
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Tidskriftsartikel (refereegranskat)abstract
- We study the uncertainty principle associated with the Klein-Gordon equation. As in the previous work [Ann. of Math. 173 (2011)], we consider vanishing along a lattice-cross. The following variants appear naturally: (1) vanishing only along "half" of the lattice-cross, where the "half" is defined as being on the boundary of a quarter-plane, and (2) that the function vanishes on the whole lattice-cross, but we require the function to have Fourier transform supported by one of the two branches of the hyperbola. In case (1) the critical phenomenon is whether the given condition forces the function to vanish on the quarter-plane in question. Here it turns out to be crucial whether the quarter-plane is space-like or time-like, and in short the answer is yes for space-like and no for time-like. The analysis brings us quite far, involving the orbit of the Hilbert kernel under the iterates of the transfer operator, and uses methods from the theory of totally positive matrices as well as Hurwitz zeta functions, and is partially postponed to a separate publication. In case (2), the critical phenomenon occurs at another density, and the dynamics then comes from the standard Gauss transformation t bar right arrow 1/t mod Z on the interval [0, 1]. In the intermediate range of the density of the lattice-cross, we obtain unique extendability of the Fourier transform from one branch of the hyperbola to the other.
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| 26. |
- Huh, June, et al.
(författare)
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Correlation bounds for fields and matroids
- 2022
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855 .- 1435-9863. ; 24:4, s. 1335-1351
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Tidskriftsartikel (refereegranskat)abstract
- Let G be a finite connected graph, and let T be a spanning tree of G chosen uniformly at random. The work of Kirchhoff on electrical networks can be used to show that the events e1 E T and e2 E T are negatively correlated for any distinct edges e1 and e2. What can be said for such events when the underlying matroid is not necessarily graphic? We use Hodge theory for matroids to bound the correlation between the events e E B, where B is a randomly chosen basis of a matroid. As an application, we prove Mason's conjecture that the number of k-element independent sets of a matroid forms an ultra-log-concave sequence in k.
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| 27. |
- Hytönen, Tuomas, et al.
(författare)
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Bounded variation approximation of Lp Dyadic martingales and solutions to elliptic equations
- 2018
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Ingår i: Journal of the European Mathematical Society. - 1435-9855 .- 1435-9863. ; 20:8, s. 1819-1850
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Tidskriftsartikel (refereegranskat)abstract
- We prove continuity and surjectivity of the trace map onto Lp(Rn), from a space of functions of locally bounded variation, defined by the Carleson functional. The extension map is constructed through a stopping time argument. This extends earlier work by Varopoulos in the BMO case, related to the Corona Theorem. We also prove LpCarleson approximability results for solutions to elliptic non-smooth divergence form equations, which generalize results in the case p = ∞ by Hofmann, Kenig, Mayboroda and Pipher.
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| 28. |
- Jochemko, Katharina, et al.
(författare)
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Combinatorial positivity of translation-invariant valuations and a discrete Hadwiger theorem
- 2018
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 20:9, s. 2181-2208
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the notion of combinatorial positivity of translation-invariant valuations on convex polytopes that extends the nonnegativity of Ehrhart h∗-vectors. We give a surprisingly simple characterization of combinatorially positive valuations that implies Stanley’s nonnegativity and monotonicity of h∗-vectors and generalizes work of Beck et al. (2010) from solid-angle polynomials to all translation-invariant simple valuations. For general polytopes, this yields a new characterization of the volume as the unique combinatorially positive valuation up to scaling. For lattice polytopes our results extend work of Betke–Kneser (1985) and give a discrete Hadwiger theorem: There is essentially a unique combinatorially-positive basis for the space of lattice-invariant valuations. As byproducts, we prove a multivariate Ehrhart–Macdonald reciprocity and we show universality of weight valuations studied in Beck et al. (2010).
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| 29. |
- Johansson, Anders, 1960-, et al.
(författare)
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Unique Bernoulli g-measures
- 2012
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 14:5, s. 1599-1615
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Tidskriftsartikel (refereegranskat)abstract
- We improve and subsume the conditions of Johansson and O¨ berg [18] and Berbee [2]for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections.In addition, we prove that these unique g-measures have Bernoulli natural extensions. In particular,we obtain a unique g-measure that has the Bernoulli property for the full shift on finitely manystates under any one of the following additional assumptions.(1)P1n=1(varn log g)2 < 1,(2) For any fixed ✏ > 0,P1n=1 e−(1/2+✏)(var1 log g+···+varn log g) = 1,(3) varn log g = o(1/pn) as n!1.That the measure is Bernoulli in the case of (1) is new. In (2) we have an improved version ofBerbee’s [2] condition (concerning uniqueness and Bernoullicity), allowing the variations of log gto be essentially twice as large. Finally, (3) is an example that our main result is new both foruniqueness and for the Bernoulli property.We also conclude that we have convergence in the Wasserstein metric of the iterates of theadjoint transfer operator to the g-measure.
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| 30. |
- Kurlberg, Pär, et al.
(författare)
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Superscars in the Seba billiard
- 2017
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863.
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Tidskriftsartikel (refereegranskat)
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