### Abstract

A method to compute the curvature of the unstable manifold is introduced and applied to Henon map and Duffing attractor, showing that it allows us to locate the homoclinic tangencies and, in turn, to construct a generating partition. The probability distribution of curvature-values is investigated, showing a power-law decay. Finally, the shape of the multifractal spectrum of effective Liapunov exponents in non-hyperbolic systems is discussed.

Original language | English |
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Pages (from-to) | 1837-1887 |

Number of pages | 51 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 24 |

Issue number | 8 |

Publication status | Published - 21 Apr 1991 |

### Keywords

- ATTRACTORS

### Cite this

*Journal of Physics A: Mathematical and General*,

*24*(8), 1837-1887.

**HOMOCLINIC TANGENCIES, GENERATING PARTITIONS AND CURVATURE OF INVARIANT-MANIFOLDS.** / GIOVANNINI, F ; POLITI, A .

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 24, no. 8, pp. 1837-1887.

}

TY - JOUR

T1 - HOMOCLINIC TANGENCIES, GENERATING PARTITIONS AND CURVATURE OF INVARIANT-MANIFOLDS

AU - GIOVANNINI, F

AU - POLITI, A

PY - 1991/4/21

Y1 - 1991/4/21

N2 - A method to compute the curvature of the unstable manifold is introduced and applied to Henon map and Duffing attractor, showing that it allows us to locate the homoclinic tangencies and, in turn, to construct a generating partition. The probability distribution of curvature-values is investigated, showing a power-law decay. Finally, the shape of the multifractal spectrum of effective Liapunov exponents in non-hyperbolic systems is discussed.

AB - A method to compute the curvature of the unstable manifold is introduced and applied to Henon map and Duffing attractor, showing that it allows us to locate the homoclinic tangencies and, in turn, to construct a generating partition. The probability distribution of curvature-values is investigated, showing a power-law decay. Finally, the shape of the multifractal spectrum of effective Liapunov exponents in non-hyperbolic systems is discussed.

KW - ATTRACTORS

M3 - Article

VL - 24

SP - 1837

EP - 1887

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 8

ER -