Periodic orbits of renormalisation for the correlations of strange nonchaotic attractors.
Mestel, B.D., Osbaldestin, A.H. (2000)
Mathematical Physics Electronic Journal [electronic only]
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Mestel, B.D., Osbaldestin, A.H. (2000)
Mathematical Physics Electronic Journal [electronic only]
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Collins, Pieter (2005)
Experimental Mathematics
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Sylvain Crovisier (2006)
Publications Mathématiques de l'IHÉS
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We prove that the chain-transitive sets of C-generic diffeomorphisms are approximated in the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense among the chain-recurrence classes. This result is a consequence of a global connecting lemma, which allows to build by a C-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff...
Boju Jiang, Seoung Ho Lee, Moo Ha Woo (2004)
Fundamenta Mathematicae
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The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Extending Ferrario's work on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets. Similar formulae for Nielsen type essential orbit numbers are also proved for fibre preserving maps.
Marek C. Zdun (1976)
Colloquium Mathematicae
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Zhen Wang, Wei Sun, Zhouchao Wei, Shanwen Zhang (2017)
Kybernetika
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Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics...
Anzelm Iwanik (1997)
Commentationes Mathematicae Universitatis Carolinae
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Let be a permutation of an abstract set . In ZFC, we find a necessary and sufficient condition it terms of cardinalities of the -orbits that allows us to topologize as a topological dynamical system on a compact Hausdorff space. This extends an early result of H. de Vries concerning compact metric dynamical systems. An analogous result is obtained for -actions without periodic points.
Starkov, Konstantin E. (2004)
Mathematical Problems in Engineering
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Aleksander Całka (1984)
Colloquium Mathematicae
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Serge Troubetzkoy (2005)
Annales de l’institut Fourier
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There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards orbits are dense in the phase space, (ii) there is a unique nonsingular perpendicular billiard orbit which is not periodic, and (iii) the perpendicular periodic orbits fill the corresponding invariant surface.