Muñoz Velazquez, Vivente and Pérez Marco, Ricardo (2011) Ergodic solenoids and generalized currents. Revista matemática complutense, 24 (2). pp. 493-525. ISSN 1988-2807
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Abstract
We introduce the concept of solenoid as an abstract laminated space. We do a thorough study of solenoids, leading to the notion of ergodic and uniquely ergodic solenoids. We define generalized currents associated with immersions of oriented solenoids endowed with a transversal measure into smooth manifolds, generalizing Ruelle-Sullivan currents.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Real homology; Ruelle-Sullivan current; Solenoid; Ergodic solenoid |
| Subjects: | Sciences > Mathematics > Differential equations |
| ID Code: | 16960 |
| References: | Dieudonné, J.: Sur le théorème de Lebesgue-Nikodym. Ann. Univ. Grenoble 23, 25–53 (1948) Hurder, S., Mitsumatsu, Y.: The intersection product of transverse invariant measures. Indiana Univ.Math. J. 40(4), 1169–1183 (1991) Moore, C., Schochet, C.: Global Analysis on Foliated Spaces. Mathematical Sciences Research Institute Publications, vol. 9. Springer, Berlin (1988) Muñoz, V., Pérez-Marco, R.: Schwartzman cycles and ergodic solenoids. In: Pardalos, P., Rassias,Th.M. (eds.) Essays in Mathematics and its Applications, Dedicated to Stephen Smale. Springer (to appear) Muñoz, V., Pérez-Marco, R.: Intersection theory for ergodic solenoids. Preprint. arXiv:0910.2915 Muñoz, V., Pérez-Marco, R.: Ergodic solenoidal homology: Realization theorem. Preprint.arXiv:0910.2913 Muñoz, V., Pérez-Marco, R.: Ergodic solenoidal homology II: Density of ergodic solenoids. Aust. J.Math. Anal. Appl. 6(1), 1–8 (2009) Muñoz, V., Pérez-Marco, R.: Hodge theory for Riemannian solenoids. In: Brzdek, J., Rassias, Th.M.(eds.) Functional Equations in Mathematical Analysis. Springer (to appear) Plante, J.F.: Foliations with measure preserving holonomy.Ann. Math. (2) 102(2), 327–361 (1975) Ruelle, D., Sullivan, D.: Currents, flows and iffeomorphisms. Topology 14(4), 319–327 (1975) Thom, R.: Sous-variétés et classes d’homologie des variétés différentiables. I. C. R. Acad. Sci. Paris 236, 453–454 (1953) Thom, R.: Sous-variétés et classes d’homologie des variétés différentiables. II. C. R. Acad. Sci. Paris 236, 573–575(1953) |
| Deposited On: | 31 Oct 2012 10:26 |
| Last Modified: | 31 Oct 2012 10:26 |
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