dynamical systems with discrete time; functional birational equations; difference equations; ordinary differential equations; partial differential equations; birational mappings; birational algebraic geometry; functional equations in number theory; integrability of birational difference, functional, ordinary and partial differential equations.
Main publications:
Rerikh K. V. General Approach to Integration of Reversible Dynamical Systems, Defined by Mappings from Cremona Group of Birational Transformation $Cr(P_k^n)$ // Matem. Zametki, 2000, 68(5), 699–799.
Rerikh K. V. Non-algebraic integrability of one reversible dynamical system of the Cremona type // J. Math. Phys., 1998, 39, 2821–2832.
Rerikh K. V. Algebraic-geometry approach to integrability of birational plane mappings. Integrable birational quadratic reversible mappings. I // J. Geometry and Physics, 1998, 24, 265–290.
Rerikh K. V. Algebraic addition concerning the Siegel theorem on the linearization of a holomorphic mapping // Math. Zeitsch., 1997, 224, 445–448.
Rerikh K. V. Non-algebraic integrability of the Chew–Low reversible dynamical system of the Cremona type and the relation with the 7th Hilbert problem (non-resonant case) // Physica D, 1995, 82, 60–78.
K. V. Rerikh, “General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group $\operatorname{Cr}(P^n_k)$ of Birational Transformations”, Mat. Zametki, 68:5 (2000), 699–709; Math. Notes, 68:5 (2000), 594–601
K. V. Rerikh, “Chew–Low equations as cremona transformations structure of general intgrals”, TMF, 50:2 (1982), 251–260; Theoret. and Math. Phys., 50:2 (1982), 164–170
V. A. Meshcheryakov, K. V. Rerikh, “Method of local construction of invariant subspaces in the solution space of Chew–Low equations”, TMF, 3:1 (1970), 78–93; Theoret. and Math. Phys., 3:1 (1971), 357–368
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