Published Papers
[1] R. De Leo, Existence and measure of ergodic leaves in Novikov's problem on the semiclassical motion of an electron, Russian Math Surveys, 56(6), 166-168, 1999, arXiv:math-ph/0005031[2] R. De Leo, Numerical analysis of the Novikov problem of a normal metal in a strong magnetic field, SIAM J. on App. Dyn. Sys., 2(4), 517-545, 2003, arXiv:math-ph/0006023
[3] R. De Leo, Characterization of ergodic regime directions in the Novikov problem of a normal metal in a strong magnetic field, Russian Math Surveys, 58(5), 1042-1043, 2003, arXiv:math/0207234v1
[4] R. De Leo, Topological effects in the magnetoresistance of Au and Ag, Physics Letters A, 332, 469-474, 2004, manuscript
[5] R. De Leo, Proof of a Dynnikov conjecture on the Novikov problem of plane sections of periodic surfaces, Russian Math Surveys, 60(3), 566-567, 2005, manuscript
[6] R. De Leo, First-principles generation of Stereographic Maps for high-field magnetoresistance in normal metals: an application to Au and Ag, Physica B, 362, 62-75, 2005, arXiv:cond-mat/0409383v1
[7] R. De Leo, Topology of plane sections of periodic polyhedra with an application to the Truncated Octahedron, Experimental Mathematics, 15(1), 109-124, 2006, arXiv:math/0502219v2
[8] M. Cadoni, R. De Leo and G. Gaeta, Solitons in a double pendulums chain model, and DNA roto-torsional dynamics, J. of Nonlinear Mathematical Physics, 14(1), 128-146, 2007, arXiv:q-bio/0604027v2
[9] M. Cadoni, R. De Leo and G. Gaeta, A composite model for DNA torsion dynamics, Phys. Rev. E, 75, 021919 (21 pages), 2007, arXiv:q-bio/0604014v2
[10] M. Cadoni, R. De Leo and G. Gaeta, A symmetry breaking mechanism for selecting the speed of relativistic solitons, J. Phys. A: Math. Theor., 40, 8517-8534, 2007, arXiv:hep-th/0702213v1
[11] M. Cadoni, R. De Leo and G. Gaeta, Sine-Gordon solitons, auxiliary fields, and singular limit of a double pendulums chain, J. Phys. A: Math. Theor., 40, 12917-12929, 2007, arXiv:0706.3173v1
[12] R. De Leo and I.A. Dynnikov, An example of fractal set of directions of planes that give a chaotic intersection with given 3-periodic surface, Russian Math Surveys, 62:5, 990-992, 2007, manuscript
[13] M. Cadoni, R. De Leo, S. Demelio and G. Gaeta, Twist solitons in complex macromolecules: from DNA to polyethylene, Int. J. on Non-Linear Mechanics, 43, 1094-1107, 2008, arXiv:0710.4475v2
[14] R. De Leo and S. Demelio, Numerical analysis of solitons profiles in a composite model for DNA torsion dynamics, Int. J. on Non-Linear Mechanics, 43, 1029-1039, 2008, arXiv:0711.1069v1
[15] R. De Leo and I.A. Dynnikov, Topology of plane sections of the infinite regular skew polyhedron {4,6|4}, Geometriae Dedicata, 138:1, 51-67, 2009, arXiv:0804.1668v1
[16] R. De Leo, A note on non-free isometric immersions, Russian Math Surveys, 63:3, 577-579, 2010, arXiv:0905.0928v1
[17] M. Cadoni, R. De Leo, S. Demelio and G. Gaeta, Propagation of twist solitons in fully inhomogeneous DNA chains, J. of Nonlinear Mathematical Physics, 17:4, 557-569, 2010, arXiv:0904.0148v1
[18] G. D'Ambra, R. De Leo and A. Loi, Partially Isometric Immersions and Free Maps, Geometriae Dedicata, 151:1, 79-95, 2011, arXiv:1007.3024v1
[19] R. De Leo, T. Gramtchev and A. Kirilov, Global Solvability in Functional Spaces for Smooth Nonsingular Vector Fields in the Plane, in "Pseudo-Differential Operators: Analysis, Applications and Computations", L. Rodino, M.W. Wong and H. Zhu eds., Springer (2011), ISBN 978-3-0348-0048-8, arXiv:1001.2121v1
[20] R. De Leo, Solvability of the cohomological equation for regular vector fields on the plane, Annals of Global Analysis and Geometry, 39:3, 231-248, 2011, arXiv:1007.3016v1
[21] M. Cadoni, R. De Leo and S. Demelio, Soliton propagation in homogeneous and non-homogeneous models for DNA torsion dynamics, Journal of Nonlinear Mathematical Physics, 18:S2, 287-319, 2011, manuscript
[22] R. De Leo, Partial immersions and partially free maps, Differential Geometry and Its Applications, 29:S1, 52-57, 2011, manuscript
[23] R. De Leo and S. Demelio, Some numerical results on motion of kinks in some model of DNA torsional dynamics", CAIM, 2:1, 18 pages, 2011
[24] R. De Leo, Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS., Journal of Geometrical Analysis, 25:3, 1798-1827, 2015, manuscript
[25] R. De Leo, A conjecture on the Hausdorff dimension of attractors of real self-projective Iterated Function Systems., Experimental Mathematics, 24:3, 270-288, 2015, manuscript
[26] R. De Leo, Weak solutions of the cohomological equation in the plane for regular vector fields, Mathematical Physics, Analysis and Geometry, 18:18, 2015, manuscript
[27] R. De Leo, C.E. Gutierrez and H. Mawi, On the Numerical Solution of the Far Field Refractor Problem, Nonlinear Analysis, 157, 123-145, 2017, arXiv:1603.01469.
[28] R. De Leo, A survey on quasiperiodic topology, Advanced Mathematical Methods in BioSciences and Applications, Eds. Berezovskaya and Toni, 2018.
[29] R. De Leo, Proof of a Gromov conjecture on the infinitesimal invertibility of the metric inducing operators, Asian Journal of Mathematics, 23:6, pp 919-932, 2019, arXiv:1711.01709
[30] R. De Leo and A.Ya. Maltsev, Quasiperiodic dynamics and magnetoresistance in normal metals, Acta Applicandae Matematicae, 162:1, pp 47-61, 2019
[31] R. De Leo, Conjectures about simple dynamics for some real Newton maps on R2, Fractals, 27:6, 2019.
[32] S.P. Novikov, R. De Leo, I.A. Dynnikov and A.Ya. Maltsev, Теория динамических систем и транспортные явления в нормальных металлах, Journal of Experimental and Theoretical Physics, 156:4, pp. 761-774, 2019 (English version)
[33] R. De Leo, Julia sets of Newton maps of real quadratic polynomial maps on the plane, Internation J. of Bifurcations and Chaos, 30:9 (2020).
[34] R. De Leo and J. Yorke, The graph of the logistic map is a tower, Discrete and Continuous Dynamical Systems, 41:11 (2021).
[35] R. De Leo and J. Yorke, Infinite towers in the graph of a dynamical system, Nonlinear Dynamics, 105 (2021).
[36] R. De Leo, Backward asymptotics in S-unimodal maps, Internation J. of Bifurcations and Chaos, 32:6 (2022).
[37] R. De Leo and J. Yorke, Streams and Graphs of Dynamical Systems, Qualitative Theory of Dynamical Systems, 24:1 (2025).
[38] Ana Anusic and R. De Leo, Graph and backward asymptotics of the tent map, accepted for publication on JDEA
Submitted
In Preparation
[39] C. Adwani, R. De Leo and J. Yorke, What is the graph of a dynamical system?.
[40] J. Auslander and R. De Leo, Wandering flows on the plane.
[41] R. De Leo, A. Loi, Uniqueness of some type of balanced metrics.
[42] R. De Leo and A. Loi, Inducing pairs metric/connections in principal bundles
Educational papers
[1] R. De Leo, An introduction to propositional logic through Smullyan's puzzles", (in italian) to appear on L'Educazione Matematica