Geodesic
Analytic Complexity: Gauge Pseudogroup, Its Orbits, and Differential Invariants
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and its applications, Tome 298 (2017), pp. 58-66

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All characteristics of analytic complexity of functions are invariant under a certain natural action (gauge pseudogroup $\mathcal G$). For the action of the pseudogroup $\mathcal G$, differential invariants are constructed and the equivalence problem is solved. Functions of two as well as of a greater number of variables are considered. Questions for further analysis are posed. 
@article{TM_2017_298_a3,
     author = {V. K. Beloshapka},
     title = {Analytic {Complexity:} {Gauge} {Pseudogroup,} {Its} {Orbits,} and {Differential} {Invariants}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {58--66},
     publisher = {mathdoc},
     volume = {298},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_298_a3/}
}
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V. K. Beloshapka. Analytic Complexity: Gauge Pseudogroup, Its Orbits, and Differential Invariants. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and its applications, Tome 298 (2017), pp. 58-66. http://geodesic.mathdoc.fr/item/TM_2017_298_a3/