World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
50
Citations
14280
World Ranking
1058
National Ranking
492

Research.com Recognitions

  • 2016 - Fellow of the American Mathematical Society For contributions to smooth dynamics and to complexity theory.
  • 2000 - Fellow of the American Association for the Advancement of Science (AAAS)
  • 1972 - Fellow of Alfred P. Sloan Foundation

Overview

Michael Shub is affiliated with the City College of New York in the United States. Their research mainly focuses on the field of Mathematics, with significant work in several subfields including Mathematical Physics, Statistical and Nonlinear Physics, Modeling and Simulation, Molecular Biology, and Geometry and Topology.

The main topics of study in Michael Shub's research encompass:

  • Mathematical Dynamics and Fractals
  • Mathematical Biology Tumor Growth
  • Gene Regulatory Network Analysis
  • Advanced Differential Equations and Dynamical Systems
  • Quantum chaos and dynamical systems
  • Random Matrices and Applications
  • Advanced Algebra and Geometry

Michael Shub has published multiple scientific papers, with notable recent contributions including:

  • "Cusp bifurcation in a metastatic regulatory network", 2023, Journal of Theoretical Biology
  • "Stable and non-symmetric pitchfork bifurcations", 2020, Science China Mathematics
  • "Cusp Bifurcation in Metastatic Breast Cancer Cells", 2022, arXiv (Cornell University)
  • "Random and mean Lyapunov exponents for GLₙ(ℝ)", 2022, arXiv (Cornell University)
  • "Random and mean Lyapunov exponents for", 2023, Ergodic Theory and Dynamical Systems

The frequent publication venues for Michael Shub's work include:

  • arXiv (Cornell University)
  • Journal of Theoretical Biology
  • Science China Mathematics
  • Ergodic Theory and Dynamical Systems

Michael Shub has collaborated extensively with several coauthors, such as:

  • Brenda Delamonica
  • Gábor Balázsi
  • Diego Armentano
  • Gautam Chinta
  • Siddhartha Sahi

Recognition for Michael Shub's contributions to mathematics includes election as:

  • Fellow of the American Mathematical Society (2016), for contributions to smooth dynamics and to complexity theory
  • Fellow of the American Association for the Advancement of Science (AAAS) (2000)
  • Fellow of Alfred P. Sloan Foundation (1972)

Best Publications

  • Complexity and Real Computation

    Lenore Blum;Felipe Cucker;Michael Shub;Steve Smale

  • A simple unpredictable pseudo random number generator

    L Blum;M Blum;M Shub

  • On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines

    Lenore Blum;Mike Shub;Steve Smale

  • Global Stability of Dynamical Systems

    Michael Shub

  • Endomorphisms of compact differentiable manifolds

    Michael Ira Shub

  • Complexity of Bezout's Theorem

    Michael Shub;Steve Smale

  • Complexity of Bézout’s theorem. I. Geometric aspects

    Michael Shub;Steve Smale

  • Newton's method on Riemannian manifolds and a geometric model for the human spine

    Roy L. Adler;Jean‐Pierre Dedieu;Joseph Y. Margulies;Marco Martens

  • Complexity of Bezout’s Theorem II Volumes and Probabilities

    Michael Shub;Steve Smale

  • How many eigenvalues of a random matrix are real

    Alan Edelman;Eric Kostlan;Michael Shub

  • Neighborhoods of hyperbolic sets

    M. Hirsch;J. Palis;C. Pugh;M. Shub

  • Complexity of Bezout's theorem IV: probability of success; extensions

    Michael Shub;Steve Smale

  • Boundary behavior of interior point algorithms in linear programming

    Nimrod Megiddo;Michael Shub

  • Complexity of Bezout's theorem V: polynomial time

    M. Shub;S. Smale

  • Pathological foliations and removable zero exponents

    Michael Shub;Amie Wilkinson

  • Stabilité globale des systèmes dynamiques

    Michael Shub

  • Stably Ergodic Dynamical Systems and Partial Hyperbolicity

    Charles Pugh;Michael Shub

  • Expanding endomorphisms of the circle revisited

    Michael Shub;Dennis Sullivan

  • Ergodicity of Anosov actions

    Charles Pugh;Michael Shub

  • Dynamical systems, filtrations and entropy

    M. Shub

Frequent Co-Authors

Felipe Cucker
Felipe Cucker City University of Hong Kong
Steve Smale
Steve Smale City University of Hong Kong
Charles Pugh
Charles Pugh University of California, Berkeley
Morris W. Hirsch
Morris W. Hirsch University of California, Berkeley
Dennis Sullivan
Dennis Sullivan Stony Brook University
Carles Simó
Carles Simó University of Barcelona
David Ruelle
David Ruelle Institut des Hautes Études Scientifiques
Chai Wah Wu
Chai Wah Wu IBM (United States)
Manuel Blum
Manuel Blum Carnegie Mellon University
Nimrod Megiddo
Nimrod Megiddo IBM (United States)

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