John M Franks

  • 1509 Citations
1969 …2019
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Research Output 1969 2019

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Article
2019
1 Citation (Scopus)

The spacetime of a shift endomorphism

Cyr, V., Franks, J. M. & Kra, B. R., Jan 1 2019, In : Transactions of the American Mathematical Society. 371, 1, p. 461-488 28 p.

Research output: Contribution to journalArticle

Endomorphism
Automorphism
Automorphism Group
Entropy
Space-time
2017

Zero entropy subgroups of mapping class groups

Franks, J. M. & Parwani, K., Feb 1 2017, In : Geometriae Dedicata. 186, 1, p. 27-38 12 p.

Research output: Contribution to journalArticle

Mapping Class Group
Pseudo-Anosov
Entropy
Subgroup
Finite Set
2013
6 Citations (Scopus)

Entropy zero area preserving diffeomorphisms of S2

Franks, J. & Handel, M., Jan 16 2013, In : Geometry and Topology. 16, 4, p. 2187-2284 98 p.

Research output: Contribution to journalArticle

Diffeomorphisms
Mapping Class Group
Entropy
Zero
Subgroup
1 Citation (Scopus)

Some virtually abelian subgroups of the group of analytic symplectic diffeomorphisms of a surface

Franks, J. M. & Handel, M., Dec 24 2013, In : Journal of Modern Dynamics. 7, 3, p. 369-394 26 p.

Research output: Contribution to journalArticle

Diffeomorphisms
Subgroup
Centralizer
Genus
Corollary
3 Citations (Scopus)

Triviality of some representations of MCG(Sg) in GL(n, C), Diff S2) and Homeo(T2)

Franks, J. M. & Handel, M., Jun 28 2013, In : Proceedings of the American Mathematical Society. 141, 9, p. 2951-2962 12 p.

Research output: Contribution to journalArticle

Homomorphism
Genus
Trivial
Mapping Class Group
Finite Type
2010
1 Citation (Scopus)

Cantor's other proofs that ℝ is uncountable

Franks, J. M., Oct 1 2010, In : Mathematics Magazine. 83, 4, p. 283-289 7 p.

Research output: Contribution to journalArticle

Cantor
Uncountable
2009
7 Citations (Scopus)

Global fixed points for centralizers and Morita's theorem

Franks, J. & Handel, M., Dec 1 2009, In : Geometry and Topology. 13, 1, p. 87-98 12 p.

Research output: Contribution to journalArticle

Centralizer
Attractor
Fixed point
Group of Diffeomorphisms
Mapping Class Group
2008

Report of the treasurer (2007)

Franks, J. M., Aug 1 2008, In : Notices of the American Mathematical Society. 55, 7, p. 858-864 7 p.

Research output: Contribution to journalArticle

2007
10 Citations (Scopus)

Fixed Points of abelian actions

Franks, J., Handel, M. & Parwani, K., 2007, In : Journal of Modern Dynamics. 1, p. 443

Research output: Contribution to journalArticle

10 Citations (Scopus)

Fixed points of abelian actions on S2

Franks, J. M., Handel, M. & Parwani, K., Oct 1 2007, In : Ergodic Theory and Dynamical Systems. 27, 5, p. 1557-1581 25 p.

Research output: Contribution to journalArticle

Common Fixed Point
Diffeomorphisms
Fixed point
Subgroup
Finitely Generated Group

Report of the treasurer (2006)

Franks, J. M., Aug 1 2007, In : Notices of the American Mathematical Society. 54, 7, p. 910-915 6 p.

Research output: Contribution to journalArticle

2006
22 Citations (Scopus)

Distortion elements in group actions on surfaces

Franks, J. M. & Handel, M., Feb 15 2006, In : Duke Mathematical Journal. 131, 3, p. 441-468 28 p.

Research output: Contribution to journalArticle

Group Action
Group of Diffeomorphisms
Borel Measure
Probability Measure
Generator

Distortion in Groups of Circle and Surface Diffeomorphisms

Crovisier, S., Franks, J., Gambaudo, J-M. & le Calvez, P., 2006, In : Dynamique des difféomorphismes conservatifs des surfaces : un point de vue topologique. 21, p. 35

Research output: Contribution to journalArticle

2003
8 Citations (Scopus)

Area preserving group actions on surfaces

Franks, J. M. & Handel, M., Jan 1 2003, In : Geometry and Topology. 7, p. 757-771 15 p.

Research output: Contribution to journalArticle

Group Action
Subgroup
Heisenberg Group
Simple group
Diffeomorphisms
8 Citations (Scopus)

Group actions on one-manifolds, II: Extensions of Hölder's theorem

Farb, B. & Franks, J. M., Nov 1 2003, In : Transactions of the American Mathematical Society. 355, 11, p. 4385-4396 12 p.

Research output: Contribution to journalArticle

Lie groups
Group Action
Theorem
Discrete Subgroup
Affine Group
25 Citations (Scopus)

Groups of homeomorphisms of one-manifolds III: Nilpotent subgroups

Farb, B. & Franks, J. M., Oct 1 2003, In : Ergodic Theory and Dynamical Systems. 23, 5, p. 1467-1484 18 p.

Research output: Contribution to journalArticle

Lie groups
Torsional stress
Subgroup
Discrete Subgroup
Torsion-free Group
43 Citations (Scopus)

Periodic points of Hamiltonian surface diffeomorphisms

Franks, J. M. & Handel, M., Jan 1 2003, In : Geometry and Topology. 7, p. 713-756 44 p.

Research output: Contribution to journalArticle

Fixed Point Set
Periodic Points
Diffeomorphism
Diffeomorphisms
Normal Form
11 Citations (Scopus)

Rotation numbers and instability sets

Franks, J. M., Jul 1 2003, In : Bulletin of the American Mathematical Society. 40, 3, p. 263-279 17 p.

Research output: Contribution to journalArticle

Rotation number
Ring or annulus
Twist Map
Geodesic Flow
Periodic Motion
2000
52 Citations (Scopus)

Shift equivalence and the Conley index

Franks, J. M. & Richeson, D., Dec 1 2000, In : Transactions of the American Mathematical Society. 352, 7, p. 3305-3322 18 p.

Research output: Contribution to journalArticle

Conley Index
Filtration
Equivalence
Invariant Set
Morse Decomposition
1999
10 Citations (Scopus)

Pseudo-anosov homeomorphisms with quadratic expansion

Franks, J. M. & Rykken, E., Dec 1 1999, In : Proceedings of the American Mathematical Society. 127, 7, p. 2183-2192 10 p.

Research output: Contribution to journalArticle

Pseudo-Anosov
Affine Structure
Branched Covering
Covering Space
Unstable Manifold
1996
38 Citations (Scopus)

Area preserving homeomorphisms of open surfaces of genus zero

Franks, J. M., Feb 5 1996, In : New York Journal of Mathematics. 2, p. 1-19 19 p.

Research output: Contribution to journalArticle

Periodic Points
Genus
Interior Point
Zero
Ring or annulus
19 Citations (Scopus)

Rotation vectors and fixed points of area preserving surface diffeomorphisms

Franks, J. M., Dec 1 1996, In : Transactions of the American Mathematical Society. 348, 7, p. 2637-2662 26 p.

Research output: Contribution to journalArticle

Diffeomorphisms
Fixed point
Diffeomorphism
Convex Hull
Interior
1992
49 Citations (Scopus)

A New Proof of the Brouwer Plane Translation Theorem

Franks, J., 1992, In : Ergodic Theory and Dynamical Systems. 12, p. 217

Research output: Contribution to journalArticle

111 Citations (Scopus)

Geodesics on S2 and periodic points of annulus homeomorphisms

Franks, J. M., Dec 1 1992, In : Inventiones Mathematicae. 108, 1, p. 403-418 16 p.

Research output: Contribution to journalArticle

Periodic Points
Ring or annulus
Geodesic
Homeomorphism
Closed Geodesics
1990
13 Citations (Scopus)

Automorphisms of one-sided subshifts of finite type

Boyle, M., Franks, J. & Kitchens, B., 1990, In : Ergodic Theory and Dynamical Systems. 10, p. 421

Research output: Contribution to journalArticle

11 Citations (Scopus)
Rotation number
Periodic Points
Diffeomorphisms
Heteroclinic Cycle
Fixed point
26 Citations (Scopus)

Rotation sets of toral flows

Franks, J. M. & Misiurewicz, M., Jan 1 1990, In : Proceedings of the American Mathematical Society. 109, 1, p. 243-249 7 p.

Research output: Contribution to journalArticle

Slope
Line segment
Line
1989
71 Citations (Scopus)

Realizing Rotation Vectors for Torus Homeomorphisms

Franks, J., 1989, In : Transactions of the American Mathematical Society. 311, p. 107

Research output: Contribution to journalArticle

1988
6 Citations (Scopus)

Entropy and exponential growth of Π1, in dimension two

Franks, J. M. & Handel, M., Jan 1 1988, In : Proceedings of the American Mathematical Society. 102, 3, p. 753-760 8 p.

Research output: Contribution to journalArticle

Topological Entropy
Diffeomorphism
Exponential Growth
Invariant Set
Finite Set
9 Citations (Scopus)

Generalizations of the Poincaré-Birkhoff Theorem

Franks, J., 1988, In : Annals of Mathematics. 128, p. 139

Research output: Contribution to journalArticle

Recurrence and Fixed Points of Surface Homeomorphisms

Franks, J., 1988, In : Ergodic Theory and Dynamical Systems. 8, p. 99

Research output: Contribution to journalArticle

1987
117 Citations (Scopus)

Braids and the jones polynomial

Franks, J. M. & Williams, R. F., Jan 1 1987, In : Transactions of the American Mathematical Society. 303, 1, p. 97-108 12 p.

Research output: Contribution to journalArticle

Jones Polynomial
Braid
Generalized Polynomials
Polynomials
Exponent
5 Citations (Scopus)

The fixed points of an analytic self-mapping

Fisher, S. D. & Franks, J. M., Jan 1 1987, In : Proceedings of the American Mathematical Society. 99, 1, p. 76-78 3 p.

Research output: Contribution to journalArticle

Riemann Surface
Fixed point
Identity function
Distinct
Hyperbolic Surface
1985
30 Citations (Scopus)

Entropy and knots

Franks, J. M. & Williams, R. F., Jan 1 1985, In : Transactions of the American Mathematical Society. 291, 1, p. 241-253 13 p.

Research output: Contribution to journalArticle

Equivalence classes
Closed Orbit
Topological Entropy
Equivalence class
Periodic Orbits
30 Citations (Scopus)

Entropy and Knots

Franks, J. & Williams, R. F., 1985, In : Transactions of the American Mathematical Society. 291, p. 241

Research output: Contribution to journalArticle

43 Citations (Scopus)

Nonsingular smale flows on S3

Franks, J. M., Jan 1 1985, In : Topology. 24, 3, p. 265-282 18 p.

Research output: Contribution to journalArticle

22 Citations (Scopus)

Period doubling and the lefschetz formula

Franks, J. M., Jan 1 1985, In : Transactions of the American Mathematical Society. 287, 1, p. 275-283 9 p.

Research output: Contribution to journalArticle

Period Doubling
Orbits
Periodic Orbits
Fixed point theorem
Orbit
22 Citations (Scopus)

Period Doubling and the Lefschetz Formula

Franks, J., 1985, In : Transactions of the American Mathematical Society. 287, p. 275

Research output: Contribution to journalArticle

1984
74 Citations (Scopus)

Flow equivalence of Subshifts of Finite Type

Franks, J., 1984, In : Ergodic Theory and Dynamical Systems. 4, p. 53

Research output: Contribution to journalArticle

Subshift
Finite Type
Equivalence
Invariant
1983
8 Citations (Scopus)

Symbolic dynamics in flows on three-manifolds

Franks, J. M., Jan 1 1983, In : Transactions of the American Mathematical Society. 279, 1, p. 231-236 6 p.

Research output: Contribution to journalArticle

Three-manifolds
Subshift
Symbolic Dynamics
Finite Type
Obstruction
8 Citations (Scopus)

Symbolic Dynamics in Flows on Three-manifolds

Franks, J., 1983, In : Transactions of the American Mathematical Society. 279, p. 231

Research output: Contribution to journalArticle

1981
5 Citations (Scopus)

An obstruction to the existence of certain dynamics in surface diffeomorphisms

Blanchard, P. & Franks, J. M., Jan 1 1981, In : Ergodic Theory and Dynamical Systems. 1, 3, p. 255-260 6 p.

Research output: Contribution to journalArticle

Diffeomorphisms
Obstruction
Subshift
Diffeomorphism
Riemann zeta function

Knots, Links, and Symbolic Dynamics

Franks, J. M., 1981, In : The Annals of Mathematics. 113, p. 529

Research output: Contribution to journalArticle

6 Citations (Scopus)

The existence of Morse-Smale diffeomorphisms

Franks, J. & Shub, M., 1981, In : Topology. 20, 3, p. 273-290 18 p.

Research output: Contribution to journalArticle

Diffeomorphisms
1980
17 Citations (Scopus)

The dynamical complexity of orientation reversing homeomorphisms of surfaces

Blanchard, P. & Franks, J. M., Jun 1 1980, In : Inventiones Mathematicae. 62, 2, p. 333-339 7 p.

Research output: Contribution to journalArticle

1979
35 Citations (Scopus)

Morse-Smale flows and homotopy theory

Franks, J. M., Jan 1 1979, In : Topology. 18, 3, p. 199-215 17 p.

Research output: Contribution to journalArticle

Homotopy Theory
1978

A reduced Zeta function for diffeomorphisms

Franks, J. M., 1978, In : American Journal of Mathematics. 100, p. 217

Research output: Contribution to journalArticle

13 Citations (Scopus)

The periodic behavior of Morse-Smale diffeomorphisms

Franks, J. M. & Narasimhan, C., Oct 1 1978, In : Inventiones Mathematicae. 48, 3, p. 279-292 14 p.

Research output: Contribution to journalArticle

Diffeomorphisms
20 Citations (Scopus)

The periodic structure of non-singular Morse-Smale flows

Franks, J., Dec 1 1978, In : Commentarii Mathematici Helvetici. 53, 1, p. 279-294 16 p.

Research output: Contribution to journalArticle

Periodic Structures
1977

Constructing structurally stable diffeomorphisms

Franks, J. M., 1977, In : Annals of Mathematics. 105, p. 343

Research output: Contribution to journalArticle