M. Martens, B. Winckler: Instability
of Renormalization,
submitted for publication.
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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.
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M. Martens, B. Winckler:
Physical Measures for infinitely renormalizable Lorenz Maps,
Ergodic Theory and Dynamical Systems, 38 (2) , 2018 , 717 - 738 |
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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 . |
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M.H. Kim, M. Martens, S. Sutherland:
Geometry of polynomials and root-finding via path-lifting,
Nonlinearity 31(2), 2018, 414-457.
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D. Gaidashev, T. Johnson, M.
Martens: Rigidity for infinitely renormalizable
area-preserving maps,
Duke Math. 165(1), 2016, 129-159.
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M. Martens, B. Winckler:
On the Hyperbolicity of Lorenz Renormalization,
Comm. Math. Phys., 325(1), (2013), 185-257. |
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P.E. Hazard, M. Lyubich, M.
Martens: Renormalisable Henon-like Maps and unbounded
geometry
Nonlinearity (2012) , 25(2), 397-420. |
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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. |
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M. Lyubich, M. Martens:
Probabilistic Universality in two-dimensional Dynamics,
Commun. Math. Phys. 383, 1295?1359 (2021). |
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M. Lyubich, M. Martens:
Renormalization in the Henon Family, II: Heteroclinic web
Invent. Math. (2011) , 186, 115-189. |
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F.H. Kwakkel, M. Martens, M.
Peixoto: Rigidity of Brillouin zones
An.
Acad. Bras. Cienc. (2011), 83(4), 1149-1158. |
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E.M. Geertsema, S. van der
Molen, M. Martens, B.L. Feringa: Optimizing Synthetic
Molecular Motors
PNAS 2009 October 6; 106(40): 16919–16924. |
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V.V.M.S. Chandramouli, M.
Martens, W. de Melo, C.P. Tresser: Chaotic period
doubling
Ergod. Th. & Dynam. Sys. (2009) 29, 381-418. |
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M. Martens, H. Meijer:
On the expected time complexisty of a heuristic maximal
Hamiltonian cycle algorithm
J.
Discrete Algorithms 2007 5(1), 102-114. |
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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. |
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J.M. Gambaudo, M. Martens:
Algebraic Topology for Minimal Cantor sets
Ann. Henri Poincare (2006) 7, 423-446. |
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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. |
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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. |
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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. |
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C. Liverani, M. Martens:
Convergence to Equilibrium for intermittent symplectic maps
Comm. Math. Phys. (2005) 260, 527-556. |
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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. |
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M. Martens, T. Nowicki:
The Ergodic Theory of One-dimensional Dynamics
IBM
J. Res. & Dev. (2003) 47 no. 1. |
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G. Birkhoff, M. Martens and C.P.
Tresser: On the scaling structure for period doubling
Asterisque (2003) 286, 167-186. |
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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. |
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M. Martens, E. Pecou, C.P.
Tresser, P. Worfolk: On the Geometry of Master-Slave
Synchronization
Chaos 12 Issue 2, (2002), 316-323. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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M. Martens, T. Nowicki:
Cycles in Newton Means
Invent. Math. 144 (2001), 225-231. |
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M. Martens, W. de Melo: Universal
Models for Lorenz Maps
Ergod. Th. & Dynam. Sys 21 (2001), 833-860. |
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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. |
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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. |
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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. |
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M. Martens, W. de Melo:
The Multipliers of Periodic Points in Interval Dynamics
Nonlinerity 12 issue 2 (1999), 217-227. |
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P. Le Calvez, M. Martens, C.
Tresser, P.A. Worfolk: Stably Non Synchronizable Maps
of the Plane
Nonlinearity 12 (january 1999), 9-18. |
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M. Martens, T. Nowicki:
Invariant Measures for Typical Quadratic Maps
Asterisque 261 (1999), 243-256. |
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M. Martens: The
Periodic Points of Renormalization
Ann. of Math. 147 (1998), 543-584. |
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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. |
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R. Galeeva, M. Martens, C.
Tresser: Inducing, Slopes and Conjugacies
Israel Journal of Mathematics 99 (1997), 123-147. |
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M. Martens:
Distortion Results and Invariant Cantor sets for Unimodal maps
Ergod. Th. & Dynam .Sys. (1994), 14, 331-349. |
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M. Martens, W. de Melo, S. van
Strien: Julia-Fatou-Sullivan theory for real
1-dimensional Dynamics
Acta Math. vol. 168 (1992), 273-318. |
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M. Martens, S. van Strien, W. de
Melo, P. Mendes: On Cherry Flows
Ergod. Th. & Dynam. Sys. 10 (1990), 531-554. |
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J.M. Aarts, M. Martens:
Flows on one-dimensional spaces
Fund. Math. 131 (1988). |
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