Geodesic
Dissipative-asymptotic manifolds
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 31 (1987), pp. 3-92

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Asymptotic analogs are considered for the fundamental concepts of differential geometry, with the role of the ring of smooth functions being played by the ring of dissipative-asymptotic functions. Among the tools developed are asymptotic changes of variables and asymptotic compositions. 
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     author = {G. A. Voropaeva and V. L. Dubnov and V. P. Maslov},
     title = {Dissipative-asymptotic manifolds},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {3--92},
     publisher = {mathdoc},
     volume = {31},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1987_31_a0/}
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G. A. Voropaeva; V. L. Dubnov; V. P. Maslov. Dissipative-asymptotic manifolds. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 31 (1987), pp. 3-92. http://geodesic.mathdoc.fr/item/INTD_1987_31_a0/