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Topological entropy of standard type monotone twist maps
| Content Provider | Semantic Scholar |
|---|---|
| Author | Knill, Oliver |
| Copyright Year | 1996 |
| Abstract | We study invariant measures of families of monotone twist maps Sγ(q, p) = (2q−p+γ ·V ′(q), q) with periodic Morse potential V . We prove that there exist a constant C = C(V ) such that the topological entropy satisfies htop(Sγ) ≥ log(C · γ)/3. In particular, htop(Sγ) → ∞ for |γ| → ∞. We show also that there exist arbitrary large γ such that Sγ has nonuniformly hyperbolic invariant measures μγ with positive metric entropy. For large γ, the measures μγ are hyperbolic and, for a class of potentials which includes V (q) = sin(q), the Lyapunov exponent of the map S with invariant measure μγ grows monotonically with γ. |
| Starting Page | 2999 |
| Ending Page | 3013 |
| Page Count | 15 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9947-96-01728-X |
| Volume Number | 348 |
| Alternate Webpage(s) | http://www.math.harvard.edu/~knill/offprints/topologicaltwist.pdf |
| Alternate Webpage(s) | http://linux46.ma.utexas.edu/mp_arc/c/95/95-192.ps.gz |
| Alternate Webpage(s) | http://abel.math.harvard.edu/~knill/offprints/topologicaltwist.pdf |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1996-348-08/S0002-9947-96-01728-X/S0002-9947-96-01728-X.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9947-96-01728-X |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
