Morris Hirsch | Academic Influence

Morris Hirsch's AcademicInfluence.com Rankings

Morris Hirsch

Mathematics

#289

World Rank

#626

Historical Rank

#140

USA Rank

Measure Theory

#356

World Rank

#530

Historical Rank

#151

USA Rank

mathematics Degrees

Download Badge

Mathematics

Morris Hirsch's Degrees

PhD Mathematics University of Chicago
Bachelors Mathematics University of Chicago

Similar Degrees You Can Earn

Best Online Bachelor's in Math 2025

Why Is Morris Hirsch Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Morris William Hirsch is an American mathematician, formerly at the University of California, Berkeley. A native of Chicago, Illinois, Hirsch attained his doctorate from the University of Chicago in 1958, under supervision of Edwin Spanier and Stephen Smale. His thesis was entitled Immersions of Manifolds. In 2012 he became a fellow of the American Mathematical Society.

(See a Problem?)

Morris Hirsch's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Differential Equations, Dynamical Systems, and Linear Algebra (1974) (2951)
The Chaos of Dynamical Systems (1985) (2137)
Differential Equations, Dynamical Systems, and an Introduction to Chaos (2003) (1306)
4. Monotone Dynamical Systems (2005) (653)
Convergent activation dynamics in continuous time networks (1989) (610)
Systems of differential equations that are competitive or cooperative. VI: A local Cr Closing Lemma for 3-dimensional systems (1985) (502)
Stability regions of nonlinear autonomous dynamical systems (1988) (435)
Systems of di erential equations which are competitive or cooperative I: limit sets (1982) (407)
Stability and convergence in strongly monotone dynamical systems. (1988) (380)
Stable manifolds for hyperbolic sets (1969) (377)
Immersions of manifolds (1959) (348)
Chain Transitivity, Attractivity, and Strong Repellors for Semidynamical Systems (2001) (202)
Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games (1999) (196)
The dynamical systems approach to differential equations (1984) (189)
Neighborhoods of hyperbolic sets (1970) (168)
Affine manifolds with nilpotent holonomy (1981) (156)
Topology of 3-Manifolds and Related Topics. (1964) (149)
The local theory of normally hyperbolic, invariant, compact manifolds (1977) (141)
Asymptotic pseudotrajectories and chain recurrent flows, with applications (1996) (136)
On Algorithms for Solving f(x)=0 (1979) (129)
SYSTEMS OF DIFFERENTIAL EQUATIONS THAT ARE COMPETITIVE OR COOPERATIVE II: CONVERGENCE ALMOST EVERYWHERE* (125)
Monotone maps: A review (2005) (108)
System of differential equations that are competitive or cooperative. IV: structural stability in three-dimensional systems (1990) (108)
Smoothings of piecewise linear manifolds (1974) (95)
Chapter 4 Monotone Dynamical Systems (2006) (88)
On imbedding di erentiable manifolds in euclidean space (1961) (86)
Smoothness of horocycle foliations (1975) (85)
The radiance obstruction and parallel forms on affine manifolds (1984) (77)
Foliated Bundles, Invariant Measures and Flat Manifolds (1975) (77)
Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn (1994) (73)
SMOOTH REGULAR NEIGHBORHOODS (1962) (70)
Competitive and Cooperative Systems: A Mini-review (2003) (69)
On the existence and classification of differentiable embeddings (1963) (64)
Immersions in the stable range (1962) (59)
Stochastic approximation algorithms with constant step size whose average is cooperative (1999) (53)
Affine manifolds and orbits of algebraic groups (1986) (53)
On existence and uniqueness of the carrying simplex for competitive dynamical systems (2008) (47)
A stable analytic foliation with only exceptional minimal sets (1975) (46)
Dynamics of Morse-Smale urn processes (1995) (46)
On combinatorial submanifolds of differentiable manifolds (1962) (43)
CONVERGENCE IN NEURAL NETS. (1987) (43)
Responses to: A. Jaffe and F. Quinn, “Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics” [Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 1–13; MR1202292 (94h:00007)] (1994) (43)
Some curious involutions of spheres (1964) (40)
A proof of the nonretractibility of a cell onto its boundary (1963) (37)
Stability of compact leaves of foliations (1973) (36)
The Imbedding of Bounding Manifolds in Euclidean Space (1961) (35)
Discrete Dynamical Systems (2013) (34)
Obstruction theories for smoothing manifolds and maps (1963) (31)
Attractors in coherent systems of differential equations (2007) (29)
Attractors for discrete-time monotone dynamical systems in strongly ordered spaces (1985) (29)
Computing with dynamic attractors in neural networks. (1995) (26)
Embeddings and compressions of polyhedra and smooth manifolds (1966) (26)
ANOSOV MAPS, POLYCYCLIC GROUPS AND HOMOLOGY (1971) (25)
Asymptotically stable equilibria for monotone semiflows (2005) (23)
Book Review: Realism in mathematics (1995) (23)
A neural network associative memory for handwritten character recognition using multiple Chua characters (1993) (22)
Stability regions of nonlinear autonomous dynamical systems - eScholarship (1988) (21)
Invariant subsets of hyperbolic sets (1971) (20)
Surgery on piecewise linear manifolds and applications (1966) (20)
Fixed points of analytic actions of supersoluble Lie groups on compact surfaces (2000) (19)
On Invariant Subsets of Hyberbolic Sets (1970) (18)
On tubular neighborhoods of piecewise linear and topological manifolds. (1968) (18)
Flat bundles with solvable holonomy (1981) (18)
ON INVOLUTIONS OF THE 3-SPHERE.* (1959) (18)
Prevalent Behavior of Strongly Order Preserving Semiflows (2006) (18)
On non-linear cell bundles (1966) (17)
ON NORMAL MICROBUNDLES (1966) (17)
Chain recurrence in surface flows (1994) (16)
Cohomology of chain recurrent sets (1988) (16)
Saturation at high gain in discrete time recurrent networks (1994) (15)
Foliations and noncompact transformation groups (1970) (15)
Polynomial forms on affine manifolds. (1982) (14)
Scissor congruence (1963) (14)
A generalization of Bieberbach's theorem (1981) (14)
On embedding 4-manifolds in R7 (1965) (14)
Affine manifolds and solvable groups (1980) (13)
Shorter Notes: A Proof of the Nonretractibility of a Cell Onto its Boundary (1963) (13)
Asymptotic phase, shadowing and reaction-diffusion systems (1993) (13)
Network Dynamics: Principles and Problems (1991) (12)
The Lorenz System (2013) (12)
STABILITY OF STATIONARY POINTS AND COHOMOLOGY OF GROUPS (1980) (11)
Flat manifolds and the cohomology of groups (1978) (11)
Invariant measures for affine foliations (1982) (11)
First-Order Equations (2013) (11)
Fixed Points of Monotone Maps (1995) (11)
Generic Quasi-convergence for Strongly Order Preserving Semiflows: A New Approach (2004) (11)
From Topology to Computation: Proceedings of the Smalefest (2011) (11)
On homotopy spheres of low dimension (1965) (10)
On piecewise regular n-knots (1964) (9)
Fixed points of local actions of nilpotent Lie groups on surfaces (2014) (9)
Positive Equilibria and Convergence in Subhomogeneous Monotone Dynamics (2020) (9)
Connected components of attractors and other stable sets (1996) (9)
On the Nonchaotic Nature of Monotone Dynamical Systems (2019) (9)
Foliated bundles, flat manifolds and invariant measures (1975) (8)
Jacobians and branch points of real analytic open maps (2002) (8)
Fixed-point indices, homoclinic contacts, and dynamics of injective planar maps. (2000) (8)
Actions of Lie groups and Lie algebras on manifolds - eScholarship (2010) (8)
Smooth actions of Lie groups and Lie algebras on manifolds (2011) (7)
On tubular neighbourhoods of manifolds. II (1966) (7)
Smoothings of Piecewise Linear Manifolds. (AM-80), Volume 80 (1975) (6)
Zero sets of Lie algebras of analytic vector fields on real and complex 2-manifolds (2013) (6)
On the fibre homotopy type of normal bundles. (1965) (6)
SATURATED OUTPUTS FOR HIGH-GAIN, SELF-EXCITING NETWORKS (1991) (6)
Foliations that are not approximable by smoother ones (1983) (6)
Smale Strategies for Network Prisoner's Dilemma Games (2015) (6)
Monotone Dynamical Systems with Polyhedral Order Cones and Dense Periodic Points (2016) (6)
Chain transitive sets for smooth strongly monotone dynamical systems (2012) (5)
Common zeroes of families of smooth vector fields on surfaces (2015) (5)
On tubular neighbourhoods of manifolds. I (1966) (5)
Learning Processes, Mixed Equilibria and Dynamical Systems (1999) (5)
Zero sets of Lie algebras of analytic vector fields on real and complex two-dimensional manifolds (2016) (5)
TOPOLOGY OF FIXED POINT SETS OF SURFACE HOMEOMORPHISMS (2000) (4)
Stability of stationary points of group actions (1979) (4)
On tangential equivalence of manifolds (1966) (4)
Degrees, Intersection Numbers, and the Euler Characteristic (1976) (4)
On tubular neighborhoods of manifolds. I (1966) (4)
Convergence in cascades of neural networks (1989) (4)
Learning Processes, Mixed Equilibria and Dynamical Systems Arising from Repeated Games (2010) (4)
On-line training of a continually adapting adaline-like network (1997) (3)
Fixed Points of Local Actions of Lie Groups on Real and Complex 2-Manifolds (2015) (3)
On imbedding differentiable manifolds in Euclidean space - eScholarship (1961) (3)
FOLIATIONS OF PLANAR REGIONS AND CCR C* ALGEBRAS WITH INFINITE COMPOSITION LENGTH (1987) (3)
The work of Stephen Smale in differential topology (1993) (3)
The qualitative analysis of a dynamical system modeling the formation of multilayer scales on pure metals (1994) (3)
Periodic orbits and homoclinic loops for surface homeomorphisms. (2005) (3)
Mathematics of Hebbian attractors (1995) (3)
ON PIECEWISE LINEAR IMMERSIONS (1965) (3)
Existence and Uniqueness Revisited (2013) (2)
On-line training of memory-driven attractor networks (1997) (2)
Immersions of almost parallelizable manifolds (1961) (2)
Stability and convergence in strongly monotone dynmamical systems (1988) (2)
7 – Nonlinear Systems (2013) (2)
COMMON FIXED POINTS FOR TWO COMMUTING SURFACE HOMEOMORPHISMS (2003) (2)
A note on the differential equations of Gleick-Lorenz (1989) (2)
ON STABILITY OF STATIONARY POINTS OF TRANSFORMATION GROUPS (1979) (2)
SMOOTHINGS OF PIECEWISE LINEAR MANIFOLDS II: CLASSIFICATION (1975) (1)
An Exact Sequence in Differential Topology (1960) (1)
Linear Algebra through Geometry. By Thomas Banchoff and John Wermer (1985) (1)
Monotone Flows with Dense Periodic Orbits (2018) (1)
Families of Morse functions parameterized by maxima. (1998) (1)
Phase Portraits for Planar Systems (2013) (1)
Stochastic Adaptive Behavior forPrisoner ' s (2007) (1)
Primary singularities of vector fields on surfaces (2018) (1)
Book Review: Geometrical methods in the theory of ordinary differential equations (1984) (1)
Closed Orbits and Limit Sets (2013) (1)
Weak limit sets of differential equations (1997) (1)
Applications of dynamical systems to deterministic and stochastic economic models (1999) (1)
Stochastic Perturbations of Dynamical Systems (1996) (1)
The linear theory of normal hyperbolicity (1977) (0)
Reminiscences of Chicago in the Fifties (1991) (0)
Primary singularities of vector fields on surfaces (2019) (0)
IMMERSIONS OF MANIFOLDSC) (1958) (0)
Common zeros of inward vector fields on surfaces (2012) (0)
Manifolds and Maps (1976) (0)
Title Zero sets of Lie algebras of analytic vector fields on real and complex two-dimensional manifolds Permalink (2017) (0)
On Involutions of the 3-Sphere Author ( s ) : (2017) (0)
Vector Bundles and Tubular Neighborhoods (1976) (0)
On tubular neighborhoods of manifolds. I - eScholarship (1966) (0)
Smoothing of piecewise liner [i.e. linear] manifolds (1964) (0)
Commentary by Ray Brown and Morris Hirsch (2016) (0)
Global Nonlinear Techniques (2013) (0)
Automorphisms of compact algebraic varieties (1993) (0)
Classification of Planar Systems (2013) (0)
SYSTEMS OF DIFFERENTIALEQUATIONS THATARE COMPETITIVEORCOOPERATIVE II: CONVERGENCEALMOSTEVERYWHERE* (1985) (0)
A lyapunov method for correlational learning in two layer neural networks (1993) (0)
A Generalization of Finite Group Theory to Finite Semigroups (2009) (0)
Prologue: Birth, Death, Time, Space, Existence, Understanding, Science, and Religion [Outline] (2009) (0)
Book Review: Computational homology (2006) (0)
M ay 2 01 8 Monotone flows with dense periodic orbits (0)
Book Review: Code recognition and set selection with neural networks (1993) (0)
Immersions of almost parallizable (1961) (0)
On the product of a contractible topological manifold and a cell (1962) (0)
The Cr section theorem and lipschitz jets (1977) (0)
Review: V. I. Arnold, Geometrical methods in the theory of ordinary differential equations (1984) (0)
Stability and convergence in strongly monotone dynmamical systems - eScholarship (1988) (0)
Dynamical Systems, Neural Networks and Cortical Models. (1994) (0)
16 – Homoclinic Phenomena (2013) (0)
Connected components of attractors and other stable sets (1996) (0)
FORUM ON MILITARY FUNDING OF MATHEMATICS (1987) (0)
On Eigenvectors of Nilpotent Lie Algebras of Linear Operators (2006) (0)
Applications in Biology (2013) (0)
1 2 N ov 2 01 8 Monotone flows with dense periodic orbits (0)
Code recognition and set selection with neural networks, by Clark Jeffries. (1988) (0)
Pseudo hyperbolicity and plaque families (1977) (0)
Common zeroes of families of smooth vector fields on surfaces (2015) (0)
Afflne manilolds with nilpotent holonomy (2007) (0)
Automata Models and the Complexity of Finite State Machines (2009) (0)
Forced smoothness of i: V → M (1977) (0)
Noncompactness and uniformity (1977) (0)
Editors' remarks (on two complexity theory surveys in the Bulletin) (1992) (0)
Applications in Mechanics (2013) (0)
Higher-Dimensional Linear Algebra (2013) (0)
Higher-Dimensional Linear Systems (2013) (0)
Planar Linear Systems (2013) (0)
ON IMBEDDING DIFFERENTIABLE MANIFOLDS (2016) (0)
The Health of Mathematics—A Second Opinion (1984) (0)
Edwin Henry Spanier (1921-1996) (1998) (0)
Surgery on piecewise linear manifolds and (2007) (0)
THE IMBEDDING OF BOUNDING MANIFOLDS IN (2016) (0)
Equilibria in Nonlinear Systems (2013) (0)
Title THE QUALITATIVE ANALYSIS OF A DYNAMICAL SYSTEM MODELING THE FORMATION OF MULTILAYER SCALES ON PURE METALS Permalink (0)
Monotone local flows with dense periodic orbits (2018) (0)
Dynamical Systems, Neural Networks and Cortical Models ASSERT 93. (1994) (0)
SMOOTHINGS OF PIECEWISE LINEAR MANIFOLDS I: PRODUCTS (1975) (0)
Zero sets of Abelian Lie algebras of vector fields (2016) (0)
What is Finite Group Theory (2009) (0)
Local product structure and local stability (1977) (0)
Let M be a manifold without boundary, of dimension n. Denote the tangent microbundle of M by TM, and the trivial microbundle (2016) (0)
Applications in Circuit Theory (2013) (0)
A Reformulation of Physics (2009) (0)
Dynamics of acyclic interval maps (2009) (0)
Continuous Direct Adaptive Control with Saturation Input Constraint (1994) (0)
Normally hyperbolic foliations and laminations (1977) (0)
Equivariant fibrations and nonwandering sets (1977) (0)
Neural Network Computing Architectures of Coupled Associative Memories with Dynamic Attractors. (1996) (0)
A Dynamic Formulation of Ring Oscillator as Solitary-Wave Propagator (1998) (0)
Learning Processes , Mixed Equilibria andDynamical Systems Arising fromRepeated (1997) (0)

This paper list is powered by the following services:

Other Resources About Morris Hirsch

en.wikipedia.org

What Schools Are Affiliated With Morris Hirsch?

Morris Hirsch is affiliated with the following schools:

Image Attributions

Image Source for Morris Hirsch