Roland Roeder: Papers

Remark on the labelling:

• Papers written while in the rank of associate professor are marked with a star (*). Papers written as a mentor are marked with a dagger (†).

Accepted Papers

• Jeffrey Diller and Roland Roeder. Equidistribution without stability for toric surface maps. To appear in Commentarii Mathematici Helvetici.
  
• Julio Rebelo and Roland Roeder. Questions about the dynamics on a natural family of affine cubic surfaces. To appear in the proceedings of the Simons Symposia on Algebraic, Complex, and Arithmetic Dynamics.
  
• Julio Rebelo and Roland Roeder. Dynamics of groups of birational automorphisms of cubic surfaces and Fatou/Julia decomposition for Painlev'e 6. To appear in the Indiana University Math Journal.
  

Published Papers

• Aneesh Dasgupta and Roland Roeder Symmetries of the Three Gap Theorem. Amer. Math. Monthly 130 (2023), no. 3, 279-284.
  This is the author's original manuscript (AOM), and this version does not include several improvements that took place due to the refereeing process.
• Alan Haynes and Roland Roeder. Level spacing statistics for the multi-dimensional quantum harmonic oscillator: algebraic case.
  J. Math. Phys. 63 (2022), no. 1, Paper No. 012102, 21 pp. (Part of the special collection in honor of Freeman Dyson at the Journal of Mathematical Physics.)
  
  

• †*1.   Ivan Chio and Roland Roeder. Chromatic Zeros On Hierarchical Lattices and Equidistribution on Parameter Space. Ann. Inst. Henri Poincaré D, 8(4): 491-536, 2021.
  
• *2.  Shu-Chiuan Chang, Roland Roeder, and Robert Shrock. q-Plane Zeros of the Potts Partition Function on Diamond Hierarchical Graphs. Journal of Mathematical Physics. 61, 073301 (2020).
  
• *3.  Luis Giraldo and Roland Roeder. Pulling back singularities of codimension one objects Proceedings of the AMS, 148(3): 1207-1217, 2020.
  
• *4.  Pavel Bleher, Mikhail Lyubich, and Roland Roeder. Lee-Yang-Fisher zeros for DHL and 2D rational dynamics, II. Global Pluripotential Interpretation. Journal of Geometric Analysis, 30(1): 777-833, 2020.
  
• †*5.  Ivan Chio, Caleb He, Anthony Ji, and Roland Roeder. Limiting Measure of Lee-Yang Zeros for the Cayley Tree. Communications in Mathematical Physics 370(3): 925-957, 2019. (Some easy proofs that were cut from the published version are still presented here.)
  
• *6.  Scott Kaschner and Roland Roeder. Complex perspective for the projective heat map acting on pentagons. Conformal Geometry and Dynamics, 21: 247-263, 2017.
• *7.  Pavel Bleher, Mikhail Lyubich, and Roland Roeder. Lee-Yang Zeros for the DHL and 2D Rational Dynamics, I. Foliation of the Physical Cylinder. Journal de Mathématiques Pures et Appliquées, 107(5): 491-590, 2017.
  
• *8.  Jeffrey Diller, Han Liu, and Roland Roeder. Typical dynamics of plane rational maps with equal degrees. Journal of Modern Dynamics, 10: 353 - 377, 2016.
  
• †*9.  Pavel Bleher, Yushi Homma, and Roland K. W. Roeder. Two-Point Correlation Functions and Universality for the Zeros of Systems of SO(n+1)-invariant Gaussian Random Polynomials International Math Research Notices (IMRN) 2016(11): 3237-3278.
  
• *10.  Scott Kaschner, Rodrigo Perez, and Roland Roeder. Examples of rational map of CP^2 with equal dynamical degrees and no invariant foliation. Bulletin de la SMF, 144(2): 279-297, 2016.
  
• 11.  Sarah Koch and Roland K. W. Roeder. Computing Dynamical Degrees. Ergodic Theory and Dynamical Systems, 36(8): 2538-2579, 2016.
  
• 12.  Roland K. W. Roeder. The action on cohomology by compositions of rational maps. Math Research Letters, 22(2):605-632, 2015.
  
• †13.  Scott R. Kaschner and Roland K.W. Roeder. Superstable manifolds of invariant circles and co-dimension 1 Bottcher functions. Ergodic Theory and Dynamical Systems, 35(1): 152 - 175, 2015.
  
• †14.  Pavel M. Bleher, Youkow Homma, Lyndon L. Ji, and Roland K.W. Roeder. Counting Zeros of Harmonic Rational Functions and Its Application to Gravitational Lensing. International Mathematics Research Notices (IMRN), 2014(8): 2265-2293.
  
• †15.  Pavel M. Bleher, Youkow Homma, Lyndon L. Ji, Roland K. W. Roeder, and Jeffrey Shen Nearest Neighbor Distances on a Circle: Multidimensional Case. Journal of Statistical Physics, 146(2): 446-465, 2012.
  
• 16.  Roland K. W. Roeder. A dichotomy for Fatou components of polynomial skew products. Conformal Geometry and Dynamics, 15: 7-19, 2011.
  
• 17.  Suzanne Lynch Hruska and Roland K. W. Roeder. Topology of Fatou components for endomorphisms of CP^k: Linking with the Green's current. Fundamenta Mathematicae, 210(1): 73-98, 2010.
  
• 18.  Enrique R. Pujals and Roland K. W. Roeder. Two Dimensional Blaschke Products: Degree Growth and Ergodic Consequences. Indiana University Mathematics Journal, 59(1): 301-326, 2010.
  
• 19.  Roland K.W. Roeder Constructing hyperbolic polyhedra using Newton's Method Experimental Mathematics, 16(4): 463-492, 2007. (See HYPER-HEDRON computer scripts.)
• 20.  Roland K.W. Roeder, John H. Hubbard, William D. Dunbar. Andreev's Theorem on Hyperbolic Polyhedra, les Annales de l'Institut Fourier, 57(3): 825-882, 2007.
• 21.  Roland K.W. Roeder Topology for the basins of attraction of Newton's Method in two complex variables: linking with currents J. Geometric Analysis. 17 (1): pp. 107-146, March 2007.
• 22.  Roland K.W. Roeder Compact hyperbolic tetrahedra with non-obtuse dihedral angles. Publicacions Matematiques, 50 (1): 211-227, 2006 .
• 23.  R.K.W. Roeder, B.I. Rapoport, and T.E. Evans Explicit calculations of homoclinic tangles in tokamaks. Physics of Plasmas, 10 (9): 3796-3799, 2003.
• 24.  Roland K.W. Roeder On Poincare's fourth and fifth examples of limit cycles at infinity, Rocky Mountain Journal of Mathematics, 33 (3): 1057-1082, 2003.

Refereed book contribution:

• *25.  Roland Roeder. Around the Boundary of Complex Dynamics (lecture notes for undergraduates). Dynamics done with your bare hands. Center for Mathematics at Notre Dame. Edited by Françoise Dal'Bo, François Ledrappier and Amie Wilkinson. EMS Series of Lectures in Mathematics Volume: 26; 2016.
  

Refereed proceedings papers:

• 26.  Omar Antolin-Camarena, Gregory R. Maloney, and Roland K.W. Roeder. Computing arithmetic invariants for hyperbolic reflection groups, In Complex Dynamics: Families and Friends (D. Schleicher editor) pages 597-631, A.K. Peters, 2008. (See SNAP-HEDRON PARI/GP computer scripts.)
• 27.  T.E. Evans, R.K.W. Roeder, J.A. Carter, and B.I. Rapoport Homoclinic Tangles, bifurcations and edge stochasticity in diverted tokamaks Contributions to Plasma Physics, 44 (1-3): 235-240, 2004.

Non-Refereed proceedings paper:

• 28.   T.E. Evans, R.K.W. Roeder, J.A. Carter, et al. Experimental signatures of homoclinic tangles in poloidally diverted tokamaks Journal of Physics: Conference Series 7 (2005) 174-190.

Non-Refereed contributing author to textbook:

• 29. Teichmuller Theory and Applications to Geometry, Topology, and Dynamics. Volume I: Teichmuller Theory by John H. Hubbard with contributions by Adrien Douady, William Dunbar, and Roland Roeder, as well as Sylvain Bonnot, David Brown, Allen Hatcher, Chris Hruska, and Sudeb Mitra. Published by Matrix Editions (2006), see http://matrixeditions.com/TeichmullerVol1.html.

Non-Refereed technical report:

• 30.   J. Mahaffy, S. W. Polk, R.K.W. Roeder An age-structured model for erythropoiesis following a phlebotomy. CRM technical report number CRM-2598, 1999.

Last updated: Feb 25th, 2024.