Nikola Petrov - Publications

(with R. de la Llave and A. Olvera)
A shadowing theorem with localization and applications to heteroclinic cycles and to properties of scaling exponents.
In progress

(with G. Alston and M. Sunkula)
Geometric quantization of focus-focus singularities.
In progress

(with D. Sheaib and A. Shapiro)
Buoyant flow of stably stratified fluid in a vertical channel with temporally periodic wall heating.
In progress

(with D. Moore-Russo)
Impact of the pandemic on the University of Oklahoma’s STEM mathematics pathway.
PRIMUS (2024) 1-14, DOI: https://doi.org/10.1080/10511970.2024.2369979
(the preprint in pdf format, a link to the published article)

(with S. Bauer)
On the existence of KAM tori for presymplectic vector fields.
Electronic Journal of Differential Equations (2020) Paper No. 126 (26 pages)
(the preprint in pdf format)

(with P. A. Nikolov)
Restriction and dimensional reduction of differential operators.
International Journal of Geometric Methods in Modern Physics 16:6 (2019) 1950094 (37 pages)
(the preprint in pdf format)

(with J. Broda and A. Grigo)
Convergence rates for semistochastic processes.
Discrete and Continuous Dynamical Systems, Series B 24:1 (2019) 109-125
(the preprint in pdf format)

Mechanics.
In Encyclopedia of Sciences and Religions, editors-in-chief A. Runehov, L. Oviedo
Springer-Verlag, 2013, ISBN: 978-1-4020-8264-1
(the preprint in pdf format)

(with P. A. Nikolov)
Dimensional reduction of invariant fields and differential operators. I. Reduction of invariant fields.
Annales Henri Poincare 13:3 (2012) 449-480
(the preprint in pdf format; a link to the published article)

(with M. Leite and E. Weng)
Stationary distributions of semistochastic processes with disturbances at random times and with random severity.
Nonlinear Analysis: Real World Applications 13:2 (2012) 497-512
(the preprint in pdf format; a link to the published article)

(with R. de la Llave and A. Olvera)
Combination laws for scaling exponents and relation to the geometry of renormalization operators.
Journal of Statistical Physics 143:5 (2011) 889-920
(the preprint in pdf format; a link to the published article)

(with J. D. Mitchell)
Temperature distribution in a uniformly moving medium.
European Journal of Physics 30:2 (2009) 417-426
(the preprint in pdf format; a link to the published article)

(with R. de la Llave)
Boundaries of Siegel disks - numerical studies of their dynamics and regularity.
Chaos 18:3 (2008) 033135 (11 pages)
(the preprint in pdf format; a link to the published article)

(with A. Olvera)
Regularity properties of critical invariant circles of twist maps, and their universality.
SIAM Journal of Applied Dynamical Systems 7:3 (2008) 962-987
(the preprint in pdf format; a link to the published article)

(with R. de la Llave and A. Olvera)
Universal scalings of universal scaling exponents.
Journal of Physics A: Mathematical and Theoretical 40:22 (2007) F427-F434
(the preprint in ps and in pdf formats; a link to the published article)

(with A. Cheskidov and C. R. Doering)
Energy dissipation in fractal-forced flow.
Journal of Mathematical Physics 48:6 (2007) 065208 (10 pages)
(the preprint in ps and in pdf formats; a link to the published article)

(with L. Lu and C. R. Doering)
Variational bounds on the energy dissipation rate in body-forced shear flow.
Journal of Turbulence 6:17 (2005) 1-17
(the preprint in ps and in pdf formats; a link to the published article)

(with C. R. Doering)
Low-wavenumber forcing and turbulent energy dissipation.
In Progress in Turbulence, Eds. J. Peinke, A. Kittel, S. Barth, M. Obelrack.
Springer-Verlag, 2005 (ISBN 3-540-23216-8), pp. 11-18
(the preprint in ps and in pdf formats)

Dynamical Casimir effect in a periodically changing domain: A dynamical systems approach.
Journal of Optics B: Quantum and Semiclassical Optics 7:3 (2005) S89-S99
(the preprint in ps and in pdf formats; a link to the published article)

(with A. Apte and R. de la Llave)
Regularity of critical invariant circles of non-twist maps.
Nonlinearity 18:3 (2005) 1173-1187
(the preprint in ps and in pdf formats; a link to the published article)

(with P. Nikolov)
A local approach to dimensional reduction. I. General formalism.
Journal of Geometry and Physics 44:4 (2003) 523-538
(the preprint in ps and in pdf formats; a link to the published article)

(with P. Nikolov)
A local approach to dimensional reduction. II. Conformal invariance in Minkowski space.
Journal of Geometry and Physics 44:4 (2003) 539-554
(the preprint in ps and in pdf formats; a link to the published article)

(with R. de la Llave and J. Vano)
Torus maps and the problem of one-dimensional optical resonator with a quasiperiodically moving wall.
Physica D 180:3-4 (2003) 140-184
(the preprint in ps and in pdf formats; a link to the published article)

(with A. B. Davis, E. E. Clothiaux, and A. Marshak)
Stratus cloud structure from mm-radar transects and satellite images: Scaling properties and artifact detection withl semi-discrete wavelet analyses.
In Proceedings of the 12th Atmospheric Radiation Measurement (ARM) Science Team Meeting (St. Petersburg, FL, April 8-12, 2002).
(the preprint in pdf format)

(with A. B. Davis and E. E. Clothiaux)
Semi-discrete wavelet characterization of stratus cloud structure from mm-radar and satellite data.
In Proceedings of the 11th American Meteorological Society Conference on Cloud Physics (Ogden, UT, June 3-7, 2002), American Meteorological Society, Boston, MA
(the preprint in ps and in pdf formats)

(with R. de la Llave)
Regularity of conjugacies between critical circle maps: An experimental study.
Experimental Mathematics 11:2 (2002) 219-241
(the preprint in ps and in pdf formats; a link to the published article

Methods of Dynamical Systems, Harmonic Analysis and Wavelets Applied to Several Physical Systems.
Ph.D. Thesis, University of Texas, Austin, 2002 (in pdf format)

(with R. de la Llave)
Theory of circle maps and the problem of one-dimensional optical resonator with a periodically moving wall.
Physical Review E 59:6 (1999) 6637-6651
(the preprint in ps and in pdf formats; a link to the published article)