Communications In Mathematical Physics - Volume 262 by M. Aizenman (Chief Editor)

By M. Aizenman (Chief Editor)

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20, 109–143 (2000) 9. : Coupled map lattices with phase transition. Nonlinearity 13, 867–888 (2000) 10. : Spatio-temporal chaos: 1. Hyperbolicity, structural stability, spatiotemporal shadowing and symbolic dynamics. Nonlinearity 6, 165–200 (1991) 11. : Spatio-temporal chaos: 2. Unique Gibbs states for higher-dimensional symbolic systems. Nonlinearity 6, 201–214 (1993) 12. : Spatio-temporal chaos: 3. Natural spatio-temporal measures for coupled circle map lattices. Nonlinearity 6, 215–230 (1993) 13.

Calabi has constructed an explicit K¨ahler–Einstein metric on del Pezzo 6 – recall that this is the blow-up of CP2 at 6 points – with a certain symmetric configuration of the 6 blown-up points. The corresponding Sasaki–Einstein metric on #6(S 2 × S 3 ) is thus also explicit. This metric has apparently never been published. –T. Yau for pointing this out to us. 2 Although one can still deduce some geometric information for the regular Sasaki–Einstein manifolds #l(S 2 × S 3 ), which are U (1) bundles over del Pezzo surfaces with l points blown up, l = 3, .

Commun. Math. Phys. : Billiards. Panor. Synth. : Invariant families of cones and Lyapunov exponents. Erg. Th. Dynam. Syst. : Principles for the design of billiards with nonvanishing Lyapunov exponents. Commum. Math. Phys. : Measure theoretic entropy of the system of hard spheres. Erg. Th. Dynam. Syst. : Linearly stable orbits in 3-dimensional billiards. Commun. Math. Phys. 129(2), 319–327 (1990) Communicated by G. Gallavotti Commun. Math. Phys. 1007/s00220-005-1474-7 Communications in Mathematical Physics Uniqueness of the SRB Measure for Piecewise Expanding Weakly Coupled Map Lattices in Any Dimension Gerhard Keller1 , Carlangelo Liverani2 1 Mathematisches Institut, Universit¨at Erlangen-N¨urnberg, Bismarckstr.

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