... Our approach involves an inducing procedure, based on the notion of hyperbolic time that we introduce here, and contains a theorem of existence of absolutely continuous invariant measure[r] ...

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... ergodic **measures** on the skew-product must be singular **with** respect to the action of the group ...of **hyperbolic** **systems** to coverings of the base space. **For** these **systems**, lifts of ...

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... author **with** P. Carrasco, we prove that if there exists an **SRB** measure then it has full ...the **systems** are skew products **for** T 2 ×T 2 ...result **for** **systems** which are not skew ...

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... dynamical **systems** have a finite number of metric attractors whose union of basins of attraction has total probability, and that each of these attractors either is a periodic orbit or supports a physical measure, ...

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... consistent **with** the physics. As in the deter- ministic case, **non**-physical **expansion** shocks occur in the stochastic case in the vicinity of sonic points; this is illustrated in the numerical ...

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... result, **for** some norm to be precised, kεW 1 k appears to be the right quantity **for** estimating the difference between the fine model and the coarse ...schemes **for** the fine model ( 1 ), we perform a ...

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... 4] **for** a complete description of the results.) **For** discretized problems, the question was solved in [ 13 ] where the author proves stability **for** **non**-zero initial data in one space ...problems ...

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... results **with** classical ADER-WENO ...approaches. **For** the test cases we carried out, the ADER-MOOD scheme requires at least 3 times less memory storage and runs 60% faster when sequential and 30% when ...

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... nonlinear **hyperbolic** **systems** of conser- vation laws in several space dimensions whose Jacobian matrices commute and, more generally, **systems** that need not be conser- ...LeFloch **for** one- ...

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... , **for** all 0 < k < n ...other **hyperbolic** properties than the local stable and unstable ...assumption **with** lim inf instead of lim sup in the definition of λ -**hyperbolic** point does not ...

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... harmonic **measures**. The usual tool **for** this kind of results is to replace the action of the group by a linear-in-time action of a dynamical system and then to apply the thermodynamic formalism to it: ...

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... L **with** coefficients in Zygmund ...symmetrizer, **for** which, then, smoothness in ξ fails to hold; in fact, we do not even have a true symmetrizer **for** our system, but just a family of approximate ...

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... used **for** all second and third order hydrodynamical simulations in this ...analysis **for** the numerical solution of the induction equation is now available, Balsara and Käppeli ...schemes **for** the ...

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... industry **for** three years, in 1980 he joined the Centre Automatique et Systèmes at École des Mines de ...Director **for** two years. In 1993, he spent a quarter at the Institute **for** Math- ematics and its ...

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... Then, in Section 3, we derive our main results: i a quite formal lower bound for the probability of observing a generic weak solution in terms of the entropy production in Section 3.1; i[r] ...

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... sofic **systems** are ...criterion **for** when the hole leads to a ...holes **with** continuous boundary) **with** corresponding topologies/**measures** to show that the “typical” hole leads to a ...set ...

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... introduced **for** ζ in a neighborhood of zero, the important linear subspaces to consider are then the positive and negative spaces of the rescaled versions of A + and A − ...well-defined, **for** ˇ τ 2 + ˇ γ 2 = ...

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... symmetrizer **for** each diagonal ...described **for** medium ...symmetrizers **for** this **hyperbolic** block needs a speciﬁc approach.For 1-D **systems**, which is our present case, the construction of ...

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... 6.3 Fully nonlinear test-cases Here we test the behavior of the scheme in the general case (1)-(2). Since the source-term depends on t, u and v, the exact integration **for** the splitting tech- nique (50) is not ...

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... approach **for** testing the last condition of Theorem 1 based on the M¨ obius transform and a critical point ...illustrated **with** explicit examples in Section ...test **for** 2-D **systems** is presented ...

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