Eintrag weiter verarbeiten
Application of hyperbolic dynamics to physics: Some problems and conjectures
Gespeichert in:
| Zeitschriftentitel: | Bulletin of the American Mathematical Society |
|---|---|
| Personen und Körperschaften: | |
| In: | Bulletin of the American Mathematical Society, 41, 2004, 3, S. 275-278 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
American Mathematical Society (AMS)
|
| Schlagwörter: |
| Zusammenfassung: | <p>The long time behavior of smooth dynamical systems is, in good cases, given by an SRB measure <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="rho"> <mml:semantics> <mml:mi>ρ<!-- ρ --></mml:mi> <mml:annotation encoding="application/x-tex">\rho</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The measure <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="rho"> <mml:semantics> <mml:mi>ρ<!-- ρ --></mml:mi> <mml:annotation encoding="application/x-tex">\rho</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is expected often to have very discontinuous dependence on parameters of the dynamical system. This is a very unsatisfactory situation for physical applications, where one would like to differentiate <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="rho"> <mml:semantics> <mml:mi>ρ<!-- ρ --></mml:mi> <mml:annotation encoding="application/x-tex">\rho</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with respect to parameters. Here we propose a solution to this difficulty, based on analytic continuation in a frequency variable <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega"> <mml:semantics> <mml:mi>ω<!-- ω --></mml:mi> <mml:annotation encoding="application/x-tex">\omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p> |
|---|---|
| Umfang: | 275-278 |
| ISSN: |
0273-0979
1088-9485 |
| DOI: | 10.1090/s0273-0979-04-01023-7 |