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 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)