Covering relations for multidimensional dynamical systems

By P. Zgliczy'nski, Marian Gidea. 2004

209 citations recorded by the source corpus.

Abstract We present a topological technique for analyzing dynamical systems with complex behavior, based on the general notion of covering relations. Our method can be used to study multidimensional dynamical systems with an arbitrary number of ‘topologically’ expanding directions.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/abeed6ef4c6d399c32f683522bb178f7d09342d7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. P. Zgliczy'nski
2. R. Llave
3. Marian Gidea

In Mathematical Physics

1. P. Zgliczy'nski
2. R. Llave
3. Marian Gidea
4. Fabio Zanolin
5. Anna Pascoletti
6. Marina Pireddu

In Statistical and Nonlinear Physics

1. P. Zgliczy'nski
2. R. Llave
3. Marian Gidea
4. Fabio Zanolin
5. Anna Pascoletti
6. Marina Pireddu

Citations in the corpus

• Covering relations, cone conditions and the stable manifold theorem (2009, methodology): “The theorem below contains a slight generalization of Theorem 9 in [ GiZ ]”
• TOPOLOGICAL METHODS IN THE INSTABILITY PROBLEM OF HAMILTONIAN SYSTEMS (2005, methodology): “The method of correctly aligned windows, as presented in [ZG04, GZ04 , GR03,”
• MULTIPLE PERIODIC SOLUTIONS AND COMPLEX DYNAMICS FOR SECOND ORDER ODES VIA LINKED TWIST MAPS (2007, background): “Wójcik [49], Kennedy and Yorke [15, 16, 17] and further developed in subsequent papers (see also [13, 14, 29, 39, 48, 58, 59, 60], just to quote some recent works in this area).”
• Rigorous numerics for dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEs (2010, methodology): “For the apparently unstable orbits we use the covering relations [30] and the Miranda Theorem [15] – see Section 10.”