Michael Shub

Mathematics · Physical Sciences

34h-index6.9kcitations168works0.02yr avg
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Research Topics

Mathematical Dynamics and Fractals(58), Quantum chaos and dynamical systems(26), Advanced Differential Equations and Dynamical Systems(25), Polynomial and algebraic computation(24), Computability, Logic, AI Algorithms(21)

Publications168 total

An average intersection estimate for families of diffeomorphisms
arXiv (Cornell University)·2024Open Access
Random and mean Lyapunov exponents for
Ergodic Theory and Dynamical Systems·2023Open Access
Cusp bifurcation in a metastatic regulatory network
Journal of Theoretical Biology·2023· 5 citedOpen Access
Random and mean Lyapunov exponents for $\mathrm{GL}_n(\mathbb{R})$
arXiv (Cornell University)·2022Open Access
Cusp Bifurcation in Metastatic Breast Cancer Cells
arXiv (Cornell University)·2022Open Access
Some Dynamics of Pseudo-Anosov Diffeomorphisms
Princeton University Press eBooks·2021· 1 cited
Stable and non-symmetric pitchfork bifurcations
Science China Mathematics·2020· 3 cited
A stable, polynomial-time algorithm for the eigenpair problem
Journal of the European Mathematical Society·2018· 18 cited
Stable and non-symmetric pitchfork bifurcations
arXiv (Cornell University)·2018Open Access
Computing the Homology of Real Projective Sets
Foundations of Computational Mathematics·2017· 2 citedOpen Access
Condition Length and Complexity for the Solution of Polynomial Systems
Foundations of Computational Mathematics·2016· 13 cited
Condition length and complexity for the solution of polynomial systems
arXiv (Cornell University)·2015Open Access
A stable, polynomial-time algorithm for the eigenpair problem
arXiv (Cornell University)·2015Open Access
Average polynomial time for eigenvector computations
arXiv (Cornell University)·2014· 3 citedOpen Access
Erratum to: Smale’s Fundamental Theorem of Algebra Reconsidered
Foundations of Computational Mathematics·2014Open Access
Periodic points on the $2$-sphere
Discrete and Continuous Dynamical Systems·2013· 10 citedOpen Access
Smale’s Fundamental Theorem of Algebra Reconsidered
Foundations of Computational Mathematics·2013· 3 cited
The complexity and geometry of numerically solving polynomial systems.
Contemporary mathematics - American Mathematical Society·2013· 8 cited
10 Some Dynamics of Pseudo-Anosov Diffeomorphisms
Princeton University Press eBooks·2012· 10 cited
The complexity and geometry of numerically solving polynomial systems
arXiv (Cornell University)·2012Open Access
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Frequent Co-authors

Charles Pugh(13), Steve Smale(9), Amie Wilkinson(5), Lenore Blum(4), Felipe Cucker(4), Morris W. Hirsch(3), Carlos Beltrán(3), Alan Edelman(2), Eric Kostlan(2), Diego Armentano(2), Peter Bürgisser(2), James Renegar(2), Nimrod Megiddo(1), Dennis Sullivan(1), M. Grayson(1), Manuel Blum(1), David Epstein(1), Jerrold E. Marsden(1), an appendix by Alexander Starkov(1), Keith Burns(1)