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Generalized Hénon difference equations with delay.

Kennedy, Judy A., Yorke, James A. (2003)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Generate $n$ -scroll attractor via composite switching controls.

Ou, Baiyu, Liu, Desheng (2010)

Mathematical Problems in Engineering

Generic chaos

Ľubomír Snoha (1990)

Commentationes Mathematicae Universitatis Carolinae

Generic diffeomorphisms on compact surfaces

Flavio Abdenur, Christian Bonatti, Sylvain Crovisier, Lorenzo J. Díaz (2005)

Fundamenta Mathematicae

We discuss the remaining obstacles to prove Smale's conjecture about the C¹-density of hyperbolicity among surface diffeomorphisms. Using a C¹-generic approach, we classify the possible pathologies that may obstruct the C¹-density of hyperbolicity. We show that there are essentially two types of obstruction: (i) persistence of infinitely many hyperbolic homoclinic classes and (ii) existence of a single homoclinic class which robustly exhibits homoclinic tangencies. In the course of our discussion,...

Generic linear cocycles over a minimal base

Jairo Bochi (2013)

Studia Mathematica

We prove that a generic linear cocycle over a minimal base dynamics of finite dimension has the property that the Oseledets splitting with respect to any invariant probability coincides almost everywhere with the finest dominated splitting. Therefore the restriction of the generic cocycle to a subbundle of the finest dominated splitting is uniformly subexponentially quasiconformal. This extends a previous result for SL(2,ℝ)-cocycles due to Avila and the author.

Generic measures for geodesic flows on nonpositively curved manifolds

Yves Coudène, Barbara Schapira (2014)

Journal de l’École polytechnique — Mathématiques

We study the generic invariant probability measures for the geodesic flow on connected complete nonpositively curved manifolds. Under a mild technical assumption, we prove that ergodicity is a generic property in the set of probability measures defined on the unit tangent bundle of the manifold and supported by trajectories not bounding a flat strip. This is done by showing that Dirac measures on periodic orbits are dense in that set.In the case of a compact surface, we get the following sharp result:...