| Autor: |
Laudenbach, François, Moraga Ferrándiz, Carlos |
| Přispěvatelé: |
Laboratoire de Mathématiques Jean Leray (LMJL), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS), Sans affiliation, European Project: 278246,EC:FP7:ERC,ERC-2011-StG_20101014,GEODYCON(2012), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), sans affiliation |
| Jazyk: |
angličtina |
| Rok vydání: |
2016 |
| Předmět: |
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| Popis: |
We consider a compact manifold of dimension greater than 2 and a differential form of degree one which is closed but non-exact. This form, viewed as a multi-valued function has a gradient vector field with respect to any Riemannian metric. After S. Novikov's work and a complement by J.-C. Sikorav, under some genericity assumptions these data yield a complex, called today the Morse-Novikov complex. Due to the non-exactness of the form, its gradient has a non-trivial dynamics in contrary to gradients of functions. In particular, it is possible that the gradient has a homoclinic orbit. The one-form being fixed, we investigate the codimension-one stratum in the space of gradients which is formed by gradients having one simple homoclinic orbit. Such a stratum S breaks up into a left and a right part separated by a substratum. The algebraic effect on the Morse-Novikov complex of crossing S depends on the part, left or right, which is crossed. The sudden creation of infinitely many new heteroclinic orbits may happen. Moreover, some gradients with a simple homoclinic orbit are approached by gradients with a simple homoclinic orbit of double energy. These two phenomena are linked. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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