Abstract:
Computer assisted proofs are becoming an important factor of present day mathematics. Since there exist short theorems having arbitrarily long proofs (a consequence of Godel's incompletness theorems, see [4, 6, 23]) and the power
Citations
|
40
|
Chaos in Lorenz equations: a computer assisted proof
– Mischaikow, Mrozek
- 1995
|
|
25
|
Isolating neighborhoods and chaos
– Mischaikow, Mrozek
- 1995
|
|
20
|
Conley index for discrete multivalued dynamical systems
– Kaczy'nski, Mrozek
- 1995
|
|
20
|
Leray Functor and the Cohomological Conley Index for Discrete Dynamical Systems
– Mrozek
- 1990
|
|
20
|
A combinatorial procedure for finding isolating neighbourhoods and index pairs
– Szymczak
- 1997
|
|
19
|
A computer-assisted proof of the Feigenbaum conjectures
– Lanford
- 1982
|
|
18
|
Topological invariants, multivalued maps and computer assisted proofs
– Mrozek
- 1996
|
|
14
|
Theorems for a price: tomorrow's semi-rigorous mathematical culture
– Zeilberger
- 1993
|
|
11
|
A computer-assisted proof of universality for areapreserving maps
– Eckmann, Koch, et al.
- 1984
|
|
11
|
The Conley index for decompositions of isolated invariant sets
– Szymczak
- 1995
|
|
8
|
A computer proof that the Lorenz equations have "chaotic
– Hassard, Hastings, et al.
- 1994
|
|
8
|
Rigorous chaos verification in discrete dynamical systems
– Neumaier, Rage
- 1993
|
|
7
|
A shooting approach to the Lorenz equations
– Hastings, Troy
- 1992
|
|
7
|
Rigorous verification of chaos in a molecular model
– Rage, Neumaier, et al.
- 1994
|
|
6
|
On a generalization of the Morse index
– Conley
- 1972
|
|
6
|
An algorithmic approach to the Conley index theory
– Mrozek
- 1999
|
|
4
|
Computer assisted proofs in analysis and programming in logic: a case study, Universite de Geneve, preprint
– Koch, Schenkel, et al.
|
|
3
|
Every planar graph is four colorable, part I: Discharging
– Appel, Haken
- 1977
|
|
3
|
Every planar graph is four colorable, part II: Reducibility
– Appel, Haken
- 1977
|
|
3
|
Existence of a homoclinic orbit of the Lorenz system by precise shooting
– Hassard, Zhang
- 1994
|
|
3
|
Short theorems with long proofs
– Spencer
- 1983
|
|
2
|
Computer assisted proofs in analysis, Physica A 124
– Lanford
- 1984
|
|
1
|
The Godel incompletness theorem from the length of proof perspective
– Dawson
- 1979
|
|
1
|
On length of proofs, Ergeb
– Godel
- 1936
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