On the polynomial entropy for morse gradient systems
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Jelena Katić
und
Milan Perić
Abstract
We adapt the construction from [HAUSEUX, L.—LE ROUX, F.: Polynomial entropy of Brouwer homeomorphisms, arXiv:1712.01502 (2017)] to obtain an easy method for computing the polynomial entropy for a continuous map of a compact metric space with finitely many non-wandering points. We compute the maximal cardinality of a singular set of Morse negative gradient systems and apply this method to compute the polynomial entropy for Morse gradient systems on surfaces.
(Communicated by Michal Fečkan)
Acknowledgement
The authors thank Frédéric Le Roux for some explanations. The authors also thank the anonymous referee for many useful comments and suggestions.
References
[1] Artigue, A.—Carrasco-Olivera, D.—Monteverde, I.: Polynomial entropy and expansivity, Acta Math. Hungar. 152 (2017), 140–149. https://doi.org/10.1007/s10474-017-0689-3.10.1007/s10474-017-0689-3Suche in Google Scholar
[2] Banyaga, A.—Hurtubise, D.: Lecture on Morse Homology. Texts Math. Sci. 29, Kluwer Academic Publisher, 2004.10.1007/978-1-4020-2696-6Suche in Google Scholar
[3] Bernard, P.—Labrousse, C.: An entropic characterization on the flat metric on the two torus, Geom. Dedicata 180 (2016), 187–201.10.1007/s10711-015-0098-0Suche in Google Scholar
[4] Eells, J.—Kuiper, N.: Manifolds which are like projective planes, Publ. Math. de I.H.E.S. 14 (1962), 5–46.10.1007/BF02684323Suche in Google Scholar
[5] Hauseux, L.—Le Roux, F.: Polynomial entropy of Brouwer homeomorphisms, arXiv:1712.01502 (2017).Suche in Google Scholar
[6] Labrousse, C.: Polynomial entropy for the circle homeomorphisms and forC1nonvanishing vector fields on 𝕋2, arXiv:1311.0213 (2013).Suche in Google Scholar
[7] Labrousse, C.: Flat metrics are strict local minimizers for the polynomial entropy, Regul. Chaotic Dyn. 17 (2012), 479–491.10.1134/S1560354712060019Suche in Google Scholar
[8] Labrousse, C.: Polynomial growth of the volume of balls for zero-entropy geodesic systems, Nonlinearity 25 (2012), 3049–3069.10.1088/0951-7715/25/11/3049Suche in Google Scholar
[9] Labrousse, C.—Marco, J. P.: Polynomial entropies for Bott integrable Hamiltonian systems, Regul. Chaotic Dyn. 19 (2014), 374–414.10.1134/S1560354714030083Suche in Google Scholar
[10] Marco, J. P.: Dynamical complexity and symplectic integrability, arXiv:0907.5363v1 (2009).Suche in Google Scholar
[11] Marco, J. P.: Polynomial entropies and integrable Hamiltonian systems, Regul. Chaotic Dyn. 18(6) (2013), 623–655.10.1134/S1560354713060051Suche in Google Scholar
[12] Palis, J.: On Morse-Smale dynamical systems, Topology 8(4) (1969), 385–404.10.1016/0040-9383(69)90024-XSuche in Google Scholar
[13] Schwarz, M.: Morse Homology. Progress in Math. 111, Birkhäuser Verlag, Basel, 1993.10.1007/978-3-0348-8577-5Suche in Google Scholar
© 2019 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
- Perfect 1-factorizations
- A topological duality for strong Boolean posets
- On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
- Tribonacci numbers and primes of the form p = x2 + 11y2
- Basic semirings
- A conjecture for varieties of completely regular semigroups
- Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
- Differential subordination results for Mittag-Leffler type functions with bounded turning property
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
- On the polynomial entropy for morse gradient systems
- Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
- A note on non-linear ∗-Jordan derivations on ∗-algebras
- Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
- Some new results on real hypersurfaces with generalized Tanaka-Webster connection
- Relative topological properties of hyperspaces
- Cohomology of torus manifold bundles
- The Menger and projective Menger properties of function spaces with the set-open topology
- Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications
Artikel in diesem Heft
- Regular papers
- The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
- Perfect 1-factorizations
- A topological duality for strong Boolean posets
- On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
- Tribonacci numbers and primes of the form p = x2 + 11y2
- Basic semirings
- A conjecture for varieties of completely regular semigroups
- Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
- Differential subordination results for Mittag-Leffler type functions with bounded turning property
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
- On the polynomial entropy for morse gradient systems
- Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
- A note on non-linear ∗-Jordan derivations on ∗-algebras
- Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
- Some new results on real hypersurfaces with generalized Tanaka-Webster connection
- Relative topological properties of hyperspaces
- Cohomology of torus manifold bundles
- The Menger and projective Menger properties of function spaces with the set-open topology
- Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications
