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Thierry Bousch
Le lemme de Mañé-Conze-Guivarc’h pour les systèmes amphidynamiques rectifiables
Annales de la faculté des sciences de Toulouse Sér. 6, 20 no. 1 (2011), p. 1-14, doi: 10.5802/afst.1284
Article: subscription required (your ip address: 54.234.42.16) | Reviews MR 2829831 | Zbl pre05903977
[Bar] Barabanov (N. E.).— On the Lyapunov exponent of discrete inclusions I, Avtomat. i Telemekh. 2 (1988), p. 40-46, traduction anglaise dans : Automat. Remote Control 49, p. 152-157 (1988). MR 940263 | Zbl 0665.93043
[Bo1] Bousch (T.).— Le poisson n’a pas d’arêtes, Ann. Inst. H. Poincaré (Proba. & Stat.) 36, p. 489-508 (2000).
Numdam | MR 1785392 | Zbl 0971.37001
[Bo2] Bousch (T.).— La condition de Walters, Ann. Sci. Ec. Norm. Sup. 34, p. 287-311 (2001).
Numdam | MR 1841880 | Zbl 0988.37036
[Bo3] Bousch (T.).— Nouvelle preuve d’un théorème de Yuan et Hunt, Bull. Soc. Math. France 136, p. 227-242 (2008). MR 2415342 | Zbl 1161.37044
[BM] Bousch (T.) & Mairesse (J.).— Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture, J. Amer. Math. Soc. 15, p. 77-111 (2002). MR 1862798 | Zbl 1057.49007
[CLT] Contreras (G.), Lopes (A.) & Thieullen (P.).— Lyapunov minimizing measures for expanding maps of the circle, Ergod. Th. Dynam. Sys. 21, p. 1379-1409 (2001). MR 1855838 | Zbl 0997.37016
[CG] Conze (J.-P.) & Guivarc’h (Y.).— Croissance des sommes ergodiques et principe variationnel, manuscrit (1993).
[Eke] Ekeland (I.).— On the variational principle, J. Math. Anal. Appl. 47, p. 324-353 (1974). MR 346619 | Zbl 0286.49015
[Fat] Fathi (A.).— Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens, C. R. Acad. Sci. Paris Math. 324 (1997). MR 1451248 | Zbl 0885.58022
[Jen] Jenkinson (O.).— On sums of powers of inverse complete quotients, Proc. Amer. Math. Soc. 136, p. 1023-1027 (2008). MR 2361877 | Zbl 1130.26011
[LS] Lawvere (F. W.) & Schanuel (S. H.).— Conceptual mathematics : a first introduction to categories, Cambridge University Press (1997). MR 1485776 | Zbl 1179.18001
[Lei] Leizarowitz (A.).— Infinite horizon autonomous systems with unbounded cost, Appl. Math. Optim. 13, p. 19-43 (1985). MR 778419 | Zbl 0591.93039
[Liv] Livšic (A. N.).— Homology properties of $Y$-systems, Math. Zametki 10 (1971), traduction anglaise dans : Math. Notes 10 (1971). MR 293669
[LT1] Lopes (A.) & Thieullen (P.).— Sub-actions for Anosov diffeomorphisms, Geometric methods in dynamics II, Astérisque 287, p. 135-146 (2003). MR 2040005 | Zbl 1045.37010
[LT2] Lopes (A.) & Thieullen (P.).— Sub-actions for Anosov flows, Ergod. Th. Dynam. Sys. 25, p. 605-628 (2005) MR 2129112 | Zbl 1078.37021
[Man] Mañé (R.).— Generic properties and problems of minimizing measures of Lagrangian systems, Nonlinearity 9, p. 273-310 (1996). MR 1384478 | Zbl 0886.58037
[Sav] Savchenko (S. V.).— Cohomological inequalities for topological Markov chains, Funkts. Anal. Prilozh. 33, p. 91-93 (1999). MR 1724277 | Zbl 0995.37001
[YH] Yuan (G.) & Hunt (B. R.).— Optimal orbits of hyperbolic systems, Nonlinearity 12, p. 1207-1224 (1999). MR 1709845 | Zbl 0951.37006
Thierry Bousch
Le lemme de Mañé-Conze-Guivarc’h pour les systèmes amphidynamiques rectifiables
Annales de la faculté des sciences de Toulouse Sér. 6, 20 no. 1 (2011), p. 1-14, doi: 10.5802/afst.1284
Article: subscription required (your ip address: 54.234.42.16) | Reviews MR 2829831 | Zbl pre05903977
Résumé - Abstract
The Mañé-Conze-Guivarc’h lemma (in Lipschitz class) is proved, for amphidynamical systems which satisfy some hyperbolicity condition, called “rectifiability”. Various applications are given.
Bibliography
[Bo1] Bousch (T.).— Le poisson n’a pas d’arêtes, Ann. Inst. H. Poincaré (Proba. & Stat.) 36, p. 489-508 (2000).
Numdam | MR 1785392 | Zbl 0971.37001
[Bo2] Bousch (T.).— La condition de Walters, Ann. Sci. Ec. Norm. Sup. 34, p. 287-311 (2001).
Numdam | MR 1841880 | Zbl 0988.37036
[Bo3] Bousch (T.).— Nouvelle preuve d’un théorème de Yuan et Hunt, Bull. Soc. Math. France 136, p. 227-242 (2008). MR 2415342 | Zbl 1161.37044
[BM] Bousch (T.) & Mairesse (J.).— Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture, J. Amer. Math. Soc. 15, p. 77-111 (2002). MR 1862798 | Zbl 1057.49007
[CLT] Contreras (G.), Lopes (A.) & Thieullen (P.).— Lyapunov minimizing measures for expanding maps of the circle, Ergod. Th. Dynam. Sys. 21, p. 1379-1409 (2001). MR 1855838 | Zbl 0997.37016
[CG] Conze (J.-P.) & Guivarc’h (Y.).— Croissance des sommes ergodiques et principe variationnel, manuscrit (1993).
[Eke] Ekeland (I.).— On the variational principle, J. Math. Anal. Appl. 47, p. 324-353 (1974). MR 346619 | Zbl 0286.49015
[Fat] Fathi (A.).— Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens, C. R. Acad. Sci. Paris Math. 324 (1997). MR 1451248 | Zbl 0885.58022
[Jen] Jenkinson (O.).— On sums of powers of inverse complete quotients, Proc. Amer. Math. Soc. 136, p. 1023-1027 (2008). MR 2361877 | Zbl 1130.26011
[LS] Lawvere (F. W.) & Schanuel (S. H.).— Conceptual mathematics : a first introduction to categories, Cambridge University Press (1997). MR 1485776 | Zbl 1179.18001
[Lei] Leizarowitz (A.).— Infinite horizon autonomous systems with unbounded cost, Appl. Math. Optim. 13, p. 19-43 (1985). MR 778419 | Zbl 0591.93039
[Liv] Livšic (A. N.).— Homology properties of $Y$-systems, Math. Zametki 10 (1971), traduction anglaise dans : Math. Notes 10 (1971). MR 293669
[LT1] Lopes (A.) & Thieullen (P.).— Sub-actions for Anosov diffeomorphisms, Geometric methods in dynamics II, Astérisque 287, p. 135-146 (2003). MR 2040005 | Zbl 1045.37010
[LT2] Lopes (A.) & Thieullen (P.).— Sub-actions for Anosov flows, Ergod. Th. Dynam. Sys. 25, p. 605-628 (2005) MR 2129112 | Zbl 1078.37021
[Man] Mañé (R.).— Generic properties and problems of minimizing measures of Lagrangian systems, Nonlinearity 9, p. 273-310 (1996). MR 1384478 | Zbl 0886.58037
[Sav] Savchenko (S. V.).— Cohomological inequalities for topological Markov chains, Funkts. Anal. Prilozh. 33, p. 91-93 (1999). MR 1724277 | Zbl 0995.37001
[YH] Yuan (G.) & Hunt (B. R.).— Optimal orbits of hyperbolic systems, Nonlinearity 12, p. 1207-1224 (1999). MR 1709845 | Zbl 0951.37006
