Publications of Marco Martens

  M. Martens, B. Winckler: Instability of Renormalization,
           submitted for publication.

  M. Martens, L. Palmisano: Invariant Manifolds for Non-Differentiable Operators,
           Trans. Amer. Math. Soc. Volume 375, Number 2, 2022, 1101-1169.

  M. Martens, L. Palmisano, B. Winckler:  The Rigidity Conjecture,
           Indagationes Mathematicae, Volume 29, Issue 3, June 2018, 825-830.

  P. Guarino, M. Martens, W. de Melo: Rigidity of critical circle maps,
           Duke Math. J. 167(11): 2018, 2125-2188.

  M. Martens, B. Winckler: Physical Measures for infinitely renormalizable Lorenz Maps,
           Ergodic Theory and Dynamical Systems, 38 (2) , 2018 , 717 - 738

  P. Hazard, M. Martens,  C. Tresser: Infinitely many moduli of stability at the dissipative boundary of chaos,
           Trans. Amer. Math. Soc. 370, 2018, 27-51 .

  M.H. Kim, M. Martens, S. Sutherland: Geometry of polynomials and root-finding via path-lifting,
           Nonlinearity 31(2), 2018, 414-457.

  D. Gaidashev, T. Johnson, M. Martens: Rigidity for infinitely renormalizable area-preserving maps,
           Duke Math. 165(1), 2016, 129-159.

  M. Martens, B. Winckler: On the Hyperbolicity of Lorenz Renormalization,
           Comm. Math. Phys.,   325(1),  (2013), 185-257.

  P.E. Hazard, M. Lyubich, M. Martens: Renormalisable Henon-like Maps and unbounded geometry
           Nonlinearity (
2012) , 25(2), 397-420.

  M. Lyubich, M. Martens: Renormalization of Henon Maps: a survey
           Dynamics, Games, and Science I, M.M. Peixoto, A.A. Pinto, D.A. Rand eds., Springer 2011, 597-618.

  M. Lyubich, M. Martens: Probabilistic Universality in two-dimensional Dynamics,
           Commun. Math. Phys. 383, 1295?1359 (2021).

  M. Lyubich, M. Martens: Renormalization in the Henon Family, II: Heteroclinic web
           Invent. Math. 
(2011) , 186, 115-189. 

  F.H. Kwakkel, M. Martens, M. Peixoto: Rigidity of Brillouin zones
           An. Acad. Bras. Cienc.
(2011), 83(4), 1149-1158.

  E.M. Geertsema, S. van der Molen, M. Martens, B.L. Feringa: Optimizing Synthetic Molecular Motors
           PNAS 2009 October 6; 106(40): 16919–16924.

  V.V.M.S. Chandramouli, M. Martens, W. de Melo, C.P. Tresser: Chaotic period doubling
           Ergod. Th. & Dynam. Sys. (2009) 29, 381-418.

  M. Martens, H. Meijer: On the expected time complexisty of a heuristic maximal Hamiltonian cycle algorithm
           J. Discrete Algorithms 2007 5(1), 102-114.

  M. Martens, V. Naudot, J. Yang: A strange attractor with large entropy in the unfolding of a low resonant degenerate homoclinic orbit
           Intern. Journ. of Bifurcation and Chaos (2006) 16, 3509-3522.

  J.M. Gambaudo, M. Martens: Algebraic Topology for Minimal Cantor sets
           Ann. Henri Poincare (2006) 7, 423-446.

  A. de Cavalho, M. Lyubich, M. Martens: Renormalization in the Henon Family, I: Universality but Non-Rigidity
           J. Stat. Phys. (2006) 121 5/6, 611-669.

  M. Martens, V. Naudot, J. Yang: A cubic Henon-like map in the unfolding of a low degenerate homoclinic orbit with resonance
           C.R. Acad. Sci. Paris, Ser. I (2005) 340, 843-846.

  R.L. Adler, B.P. Kitchens, M. Martens, C. Pugh, M. Shub, C.P. Tresser: Convex dynamics and applications
           Ergod. Th.& Dynam. Sys. (2005) 25, 321-352.

  C. Liverani, M. Martens: Convergence to Equilibrium for intermittent symplectic maps
           Comm. Math. Phys. (2005) 260, 527-556.

  R. Adler, B. Kitchens, M. Martens, C.P. Tresser, C.W. Wu: The mathematical theory of printing
           IBM J. Res. & Dev. (2003) 47 no. 1.

  M. Martens, T. Nowicki: The Ergodic Theory of One-dimensional Dynamics
           IBM J. Res. & Dev. (2003) 47 no. 1.

  G. Birkhoff, M. Martens and C.P. Tresser: On the scaling structure for period doubling
           Asterisque (2003) 286, 167-186.

  T. Nowicki, J.Q. Trelewicz, M. Martens, T. Trenary: Error Diffusion Method for Resampling in the Transform domain
           International Journal of Computational and Numerical Analysis and Applications, vol. 2, no. 4, 2002, pp. 413-427.

  M. Martens, E. Pecou, C.P. Tresser, P. Worfolk: On the Geometry of Master-Slave Synchronization
           Chaos 12 Issue 2, (2002), 316-323.

  R. Adler, J.P. Dedieu, J. Margulis, M. Martens, M. Shub: Newton's Method on Riemannian Manifolds and a Geometrical Model for the Human Spine
           IMA journal of Numerical Analysis, 2 Issue 3, (2002), 359-390.

  R. Adler, B. Kitchens, M. Martens, A. Nogueira, C.P. Tresser, C.W. Wu: Error Bounds for error diffusion and Related Halftoning Algorithm
           Proceedings of the IEEE INternational Symposium on Circuits and Systems (2001) II,513-516.

  T. Trenary, A. Michelli,J.Q. Trelewicz, M. Martens, J.L. Mitchell: Fast DCT-domain image shifting and merging
           Proceedings of 35th Asilomar Conference on Signals, Systems, and Computers 2001, (Pacific Grove, CA), 4-7 Nov 2001.

  R.L Adler, J.Y. Margulies, M. Martens, M. Shub: The Scoliotic Curve: Correlation to the Deformity of Individual Vertebrae
           European Spine Journal Vol 10 supplement 1 (2001), 45.

  R.L Adler, J.Y. Margulies, M. Martens, M. Shub: Mathematical Tool for Planning Surgical Corrections and Spine Balance
           European Spine Journal Vol 10 supplement 1 (2001), 9.

  M. Martens, A. de Melo, W. de Melo: On the dynamics of the renormalization operator
           Global Analysis of Dynamical Systems, Festschrift dedicated to Floris Takens for his 60th birthday, IOP publishing Ltd 2001, 449-461.

  M. Martens, T. Nowicki: Cycles in Newton Means
           Invent. Math. 144 (2001), 225-231.

  M. Martens, W. de Melo: Universal Models for Lorenz Maps
           Ergod. Th. & Dynam. Sys 21 (2001), 833-860.

  J.Y. Margulis, R.L. Adler, A.D. Kalvin, M. Martens, M. Shub, C.P. Tresser, C.W. Wu: Deforming Factors in Indopathic Scoliosis: a mathematical tool
           SPINE: State of the Art Reviews, vol. 14, no. 2, 505-509, 2000.

  R. Adler, B. Kitchens, M. Martens, A. Nogueira, C.P. Tresser, C.W.Wu: Error Bounds for error diffusion and other mathematical problems arising in digital halftoning
           IS\&T/SPIE's int. Symp. Elec. Imaging, San Jose, CA, vol. 3963, 437-443,2000.

  N.J. Balmforth, A. Provenzale, E.A. Spiegel, M. Martens, C. Tresser, C.W. Wu: Red Spectra from White and Blue Noise
           Proceedings of the Royal Society: Biological Science, 266, no.1416 (1999) 311.

  M. Martens, W. de Melo: The Multipliers of Periodic Points in Interval Dynamics
           Nonlinerity 12 issue 2 (1999), 217-227.

  P. Le Calvez, M. Martens, C. Tresser, P.A. Worfolk: Stably Non Synchronizable Maps of the Plane
           Nonlinearity 12 (january 1999), 9-18.

  M. Martens, T. Nowicki: Invariant Measures for Typical Quadratic Maps
           Asterisque 261 (1999), 243-256.

  M. Martens: The Periodic Points of Renormalization
           Ann. of Math. 147 (1998), 543-584.

  M. Martens, C.P. Tresser: Forcing of Periodic Orbits for Interval Maps and Renormalization of Piecewise Affine Maps
           Proc. Amer. Math. Soc. 124 No. 9 (1996) 2863-2870.

  R. Galeeva, M. Martens, C. Tresser: Inducing, Slopes and Conjugacies
           Israel Journal of Mathematics 99 (1997), 123-147.

  M. Martens: Distortion Results and Invariant Cantor sets for Unimodal maps
           Ergod. Th. & Dynam .Sys. (1994), 14, 331-349.

  M. Martens, W. de Melo, S. van Strien: Julia-Fatou-Sullivan theory for real 1-dimensional Dynamics
           Acta Math. vol. 168 (1992), 273-318.

  M. Martens, S. van Strien, W. de Melo, P. Mendes: On Cherry Flows
           Ergod. Th. & Dynam. Sys. 10 (1990), 531-554.

  J.M. Aarts, M. Martens: Flows on one-dimensional spaces
           Fund. Math. 131 (1988).